intersection of parametric lines calculator10 marca 2023
Conic Sections: Parabola and Focus. @bd1251252 The two lines intersect when they have the same values. Consider the line given by \(\eqref{parameqn}\). This article can be a great way to check your work or to see how to Find the intersection of two parametric lines. Articles that describe this calculator Equation of a line given two points Parametric line equation from two points First Point x y Second point x y Equation for x Equation for y Direction vector Calculation precision Digits after the decimal point: 2 Point of Intersection of two lines calculator. But I don't see how this gives me a point of intersection. An online calculator to find and graph the intersection of two lines. \newcommand{\fermi}{\,{\rm f}}% Work on the task that is enjoyable to you. Flipping to the back it tells me that they do intersect and at the point $(2,3,1).$ How did they arrive at this answer? Let \(\vec{d} = \vec{p} - \vec{p_0}\). \newcommand{\sech}{\,{\rm sech}}% The vector equation for the line of intersection is calculated using a point on the line and the cross product of the normal vectors of the two planes. This equation determines the line \(L\) in \(\mathbb{R}^2\). Man oh man. Angle Between Two Lines Formula Derivation And Calculation. Not only that, but it has amazing features other calculators don't have. Then \(\vec{d}\) is the direction vector for \(L\) and the vector equation for \(L\) is given by \[\vec{p}=\vec{p_0}+t\vec{d}, t\in\mathbb{R}\nonumber \]. - the incident has nothing to do with me; can I use this this way? What makes two lines in 3-space perpendicular? Therefore it is not necessary to explore the case of \(n=1\) further. $$y_1=y_2\Longrightarrow3=2s+3,$$ \newcommand{\pars}[1]{\left( #1 \right)}% They want me to find the intersection of these two lines: To determine what the math problem is, you will need to take a close look at the information given and use your problem-solving skills. It gives me the steps that how a sum is solved, i LOVE this it helps me on homework so I can understand what I need to do to get the answer and the best thing is that it has no ads. This tool calculates 3d line equations : parametric, cartesian and vector equations. parametric equation: Consider the following definition. parametric equation: Figure out mathematic question Math is a challenging subject for many students, but with practice and persistence, anyone can learn to figure out complex equations. It's is amazing and helpful but sadly if u want full explanation u need to pay with money. [2] 2021/05/03 01:52 40 years old level / An engineer / Useful / Intersection of two parametric lines calculator - They intersect each other when all their coordinates are the same. So no solution exists, and the lines do not intersect. Learn more about Stack Overflow the company, and our products. Why do small African island nations perform better than African continental nations, considering democracy and human development? An online calculator to find and graph the intersection of two lines. L_1:x=4t+2,y=3,z=-t+1,\\ Provides step by step easy solutions for the problems so that it becomes really easy to understand. In the plane, lines can just be parallel, intersecting or equal. 2-3a &= 3-9b &(3) Stey by step. How can I check before my flight that the cloud separation requirements in VFR flight rules are met? Consider the following diagram. An intersection point of 2 given relations is the. This page titled 4.6: Parametric Lines is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Ken Kuttler (Lyryx) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. In the following example, we look at how to take the equation of a line from symmetric form to parametric form. No matter what the task is, if it is something that you are passionate about, you will be able to work on it with ease and produce great results. Intersection of two parametric lines calculator - Best of all, Intersection of two parametric lines calculator is free to use, so there's no reason not to give . Two equations is (usually) enough to solve a system with two unknowns. Note: the two parameters JUST HAPPEN to have the same value this is because I picked simple lines so. Flipping to the back it tells me that they do intersect and at the point $ (2,3,1).$ How did they arrive at this answer? If $\ds{0 \not= -B^{2}D^{2} + \pars{\vec{B}\cdot\vec{D}}^{2} Now consider the case where \(n=2\), in other words \(\mathbb{R}^2\). You want to know about a certain topic? Sets Intersect Calculator Intersect two or more sets step-by-step Most Used Actions Related Number Line Graph Examples Related Symbolab blog posts We. \newcommand{\root}[2][]{\,\sqrt[#1]{\,#2\,}\,}% Enter two lines in space. If we know the direction vector of a line, as well as a point on the line, we can find the vector equation. \newcommand{\ket}[1]{\left\vert #1\right\rangle}% $$ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. if $s=0$, are (2,3,1) just like the answer. Are there tables of wastage rates for different fruit and veg? Mathematical tasks can be difficult to figure out, but with perseverance and a little bit of help, they can be conquered. Modified 5 years, . These lines are in R3 are not parallel, and do not intersect, and so 11 and 12 are skew lines. Best of all, Angle of intersection between two parametric curves calculator is free to use, so there's no reason not to give it a try! However, consider the two line segments along the x-axis (0,0->1,0) and (1,0 ->2,0). $$z_1=z_2\Longrightarrow1-t=s+1.$$, In this case, if we set both parameters equal to zero, the system will be solved. \vec{B}\cdot\vec{D}\ t & - & D^{2}\ v & = & \pars{\vec{C} - \vec{A}}\cdot\vec{D} Can airtags be tracked from an iMac desktop, with no iPhone? Intersection of two lines calculator with detailed, step by step explanation show help examples Input lines in: Enter first line: Enter second line: Type r to input square roots . \newcommand{\bracks}[1]{\left\lbrack #1 \right\rbrack}% An online calculator to find and graph the intersection of two lines. Linear Algebra - Linear transformation question. parametric equation: Algebra 1 module 4 solving equations and inequalities, Find the lengths of the missing sides of the triangle write your answers, Great british quiz questions multiple choice, How to get a position time graph from a velocity time graph, Logistic equation solver with upper and lower bounds, Natural deduction exercises with solutions, Solve quadratic equation using graphing calculator. \newcommand{\floor}[1]{\,\left\lfloor #1 \right\rfloor\,}% math is the study of numbers, shapes, and patterns. \left\lbrace% It also plots them on the graph. If you're struggling to clear up a math equation, try breaking it down into smaller, more manageable pieces. Thus, you have 3 simultaneous equations with only 2 unknowns, so you are good to go! You can solve for the parameter \(t\) to write \[\begin{array}{l} t=x-1 \\ t=\frac{y-2}{2} \\ t=z \end{array}\nonumber \] Therefore, \[x-1=\frac{y-2}{2}=z\nonumber \] This is the symmetric form of the line. B^{2}\ t & - & \vec{D}\cdot\vec{B}\ v & = & \pars{\vec{C} - \vec{A}}\cdot\vec{B} $$y_1=y_2\Longrightarrow3=3,$$ Math can be a difficult subject for many people, but there are ways to make it easier. In order to find the point of intersection we need at least one of the unknowns. \newcommand{\iff}{\Longleftrightarrow} How do you do this? Find a vector equation for the line through the points \(P_0 = \left( 1,2,0\right)\) and \(P = \left( 2,-4,6\right).\), We will use the definition of a line given above in Definition \(\PageIndex{1}\) to write this line in the form, \[\vec{q}=\vec{p_0}+t\left( \vec{p}-\vec{p_0}\right)\nonumber \]. The calculator displays the canonical and parametric equations of the line, as well as the coordinates of the point belonging to the line and the direction vector of the line. Free line intersection calculator This calculator will find out what is the intersection point of 2 functions or relations are. Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to find point of two lines intersection. Do I need a thermal expansion tank if I already have a pressure tank? Mathepower finds out if and where they intersect. We have the system of equations: $$ Why are Suriname, Belize, and Guinea-Bissau classified as "Small Island Developing States"? This calculator will find out what is the intersection point of 2 functions or relations are. Ex 2: Find the Parametric Equations of the Line of Intersection Multivariable Calculus: Are the planes 2x - 3y + z = 4 and x - y +z = 1 find the equation of the line of intersection in parametric and s. . \end{aligned} Point of intersection parametric equations calculator - Do the lines intersect at some point, and if so, which point? Is there a proper earth ground point in this switch box? Given two lines to find their intersection. = -\pars{\vec{B} \times \vec{D}}^{2}}$ which is equivalent to: . \newcommand{\totald}[3][]{\frac{{\rm d}^{#1} #2}{{\rm d} #3^{#1}}} In 3 dimensions, two lines need not intersect. Let \(\vec{q} = \left[ \begin{array}{c} x \\ y \\ z \end{array} \right]B\). The Intersection of Two Planes Calculator: Find the Point of Find the point of two lines intersection. Suppose the symmetric form of a line is \[\frac{x-2}{3}=\frac{y-1}{2}=z+3\nonumber \] Write the line in parametric form as well as vector form. \newcommand{\pp}{{\cal P}}% An online calculator to find the point of intersection of two lines in 3D is presented. Point of Intersection of Two Lines in 3D The equation in vector form of a line throught the points A(xA, yA, zA) and B(xB, yB, zB) is written as < x, y, z > = < xA, yA, zA > + t < xB xA, yB yA, zB zA > (I) The only thing I see is that if the end numbers on $s$, i.e. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. $$ L_2:x=2s+2,y=2s+3,z=s+1. * Is the system of equations dependent, independent, or inconsistent. U always think these kind of apps are fake and give u random answers but it gives right answers and my teacher has no idea about it and I'm getting every equation right. This is of the form \[\begin{array}{ll} \left. +1, Determine if two straight lines given by parametric equations intersect, We've added a "Necessary cookies only" option to the cookie consent popup. First step is to isolate one of the unknowns, in this case t; t= (c+u.d-a)/b. They may either intersect, then their interse Calculator will generate a step-by-step explanation. . Using indicator constraint with two variables, Is there a solution to add special characters from software and how to do it. 2D and 3D Vectors This online calculator will help you to find angle between two lines. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Time to time kinds stupid but that might just be me. It's amazing it helps so much and there's different subjects for your problems and taking a picture is so easy. To find out if they intersect or not, should i find if the direction vector are scalar multiples? You can see that by doing so, we could find a vector with its point at \(Q\). The best answers are voted up and rise to the top, Not the answer you're looking for? Equation of the 1st line: y = x +. which is false. Stey by step. The reason for this terminology is that there are infinitely many different vector equations for the same line. They want me to find the intersection of these two lines: \begin {align} L_1:x=4t+2,y=3,z=-t+1,\\ L_2:x=2s+2,y=2s+3,z=s+1. For which values of d, e, and f are these vectors linearly independent? This has saved me alot of time in school. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. d. Intersection of two parametric lines calculator - One tool that can be used is Intersection of two parametric lines calculator. In order to determine what the math problem is, you will need to look at the given information and find the key details. $$x_1=x_2\Longrightarrow2=2,$$ we can find the pair $\pars{t,v}$ from the pair of equations $\pars{1}$. \newcommand{\imp}{\Longrightarrow}% I can't believe I have to scan my math problem just to get it checked. You can improve your academic performance by studying regularly and attending class. We can use the above discussion to find the equation of a line when given two distinct points. The best way to download full math explanation, it's download answer here. Then, \(L\) is the collection of points \(Q\) which have the position vector \(\vec{q}\) given by \[\vec{q}=\vec{p_0}+t\left( \vec{p}-\vec{p_0}\right)\nonumber \] where \(t\in \mathbb{R}\). $$, $-(2)+(1)+(3)$ gives <4,-3,2>+t<1,8,-3>=<1,0,3>+v<4,-5,-9> iff 4+t=1+4v and -3+8t+-5v and if you simplify the equations you will come up with specific values for v and t (specific values unless the two lines are one and the same as they are only lines and euclid's 5th), I like the generality of this answer: the vectors are not constrained to a certain dimensionality. Then, we can find \(\vec{p}\) and \(\vec{p_0}\) by taking the position vectors of points \(P\) and \(P_0\) respectively. A Parametric Equation Calculator is used to calculate the results of parametric equations corresponding to a Parameter . parametric equation: Given through two points to be equalized with line Choose how the second line is given. Everyone who receives the link will be able to view this calculation, Copyright PlanetCalc Version:
You also can solve for t in any of the, Absolute value inequalities with no solution, How to add integers without using number line, How to calculate square footage around a pool, How to solve log equations with different bases, How to solve systems of equations by substitution with 2 variables. Find the intersection of two circles. 1. On the stereonet graphically enter the location of two planes. The average passing rate for this test is 82%. Let \(L\) be a line in \(\mathbb{R}^3\) which has direction vector \(\vec{d} = \left[ \begin{array}{c} a \\ b \\ c \end{array} \right]B\) and goes through the point \(P_0 = \left( x_0, y_0, z_0 \right)\). Is there a single-word adjective for "having exceptionally strong moral principles"? The calculator displays the canonical and parametric equations of the line, as well as the coordinates of the point belonging to the line and the direction vector of the line. Why did Ukraine abstain from the UNHRC vote on China? Once you have found the key details, you will be able to work out what the problem is and how to solve it. \newcommand{\ceil}[1]{\,\left\lceil #1 \right\rceil\,}% Good helper, it is fast and also shows you how to do the equation step by step in detail to help you learn it, this app is amazing! This online calculator finds parametric equations for a line passing through the given points. Intersection of two lines calculator Do the lines intersect at some point, and if so, which point? Here, the direction vector \(\left[ \begin{array}{r} 1 \\ -6 \\ 6 \end{array} \right]B\) is obtained by \(\vec{p} - \vec{p_0} = \left[ \begin{array}{r} 2 \\ -4 \\ 6 \end{array} \right]B - \left[ \begin{array}{r} 1 \\ 2 \\ 0 \end{array} \right]B\) as indicated above in Definition \(\PageIndex{1}\). Timely deadlines. * Is the system of equations dependent, . Consider the following example. In fact, it determines a line \(L\) in \(\mathbb{R}^n\). This app is really good. $$ This app is very helpful for me since school is back around, app gives detailed solutions to problems to help you study for your test, the best app for solving math problems,and a great app for students, i thank all the members of the This app group for your support to students like me. \vec{A} + t\,\vec{B} = \vec{C} + v\,\vec{D}\quad\imp\quad Then, \[\vec{q}=\vec{p_0}+t\left( \vec{p}-\vec{p_0}\right)\nonumber \] can be written as, \[\left[ \begin{array}{c} x \\ y \\ z \\ \end{array} \right]B = \left[ \begin{array}{c} 1 \\ 2 \\ 0 \end{array} \right]B + t \left[ \begin{array}{r} 1 \\ -6 \\ 6 \end{array} \right]B, \;t\in \mathbb{R}\nonumber \]. \begin{array}{c} x=2 + 3t \\ y=1 + 2t \\ z=-3 + t \end{array} \right\} & \mbox{with} \;t\in \mathbb{R} \end{array}\nonumber \]. Are parallel vectors always scalar multiple of each others? Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. \begin{array}{rcrcl}\quad Stey by step. Choose how the first line is given. This is the parametric equation for this line. Find more Mathematics widgets in Wolfram|Alpha. Intersection of two lines calculator 1 Answer. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. To embed this widget in a post on your WordPress blog, copy and paste the shortcode below into the HTML source: To add a widget to a MediaWiki site, the wiki must have the. Choose how the first line is given. Vector Line And Plane Equation A Level Maths Uptuition With Mr Will. It is used in everyday life, from counting to measuring to more complex calculations. \newcommand{\ol}[1]{\overline{#1}}% Using Kolmogorov complexity to measure difficulty of problems? It works also as a line equation converter. \newcommand{\angles}[1]{\left\langle #1 \right\rangle}% Ask Question Asked 9 years, 2 months ago. Very easy to use, buttons are layed out comfortably, and it gives you multiple answers for questions. $\endgroup$ - wfw. As usual, you can find the theory, How do you simplify a square root expression, How to get rid of restricted values in excel, Potential energy to kinetic energy converter, What does perpendicular mean in a math problem. 3d Line Calculator. Created by Hanna Pamua, PhD. $\newcommand{\+}{^{\dagger}}% This is not a question on my homework, just one from the book I'm trying to figure out. This high rating indicates that the company is doing a good job of meeting customer needs and expectations. The two lines are the linear equations with degree 1. I think they are not on the same surface (plane). 24/7 support \newcommand{\ds}[1]{\displaystyle{#1}}% @bd1251252 take a look at the second equation. Note that this definition agrees with the usual notion of a line in two dimensions and so this is consistent with earlier concepts. -3+8a &= -5b &(2) \\ Given two lines to find their intersection. By inspecting the parametric equations of both lines, we see that the direction vectors of the two lines are not scalar multiples of each other, so the lines are not parallel. Then, letting \(t\) be a parameter, we can write \(L\) as \[\begin{array}{ll} \left. The two lines intersect if and only if there are real numbers $a$, $b$ such that $[4,-3,2] + a[1,8,-3] = [1,0,3] + b[4,-5,-9]$. Different parameters must be used for each line, say s 876+ Math Experts 99% Improved Their Grades Know is an AI-powered content marketing platform that makes it easy for businesses to create and distribute high-quality content. . This online calculator finds and displays the point of intersection of two lines given by their equations. If you're looking for help with your homework, our team of experts have you covered. $$x_1=x_2\Longrightarrow4t+2=2s+2,$$ What is a word for the arcane equivalent of a monastery? Moreover, it describes the linear equations system to be solved in order to find the solution. Then solving for \(x,y,z,\) yields \[\begin{array}{ll} \left. This calculator will find out what is the intersection point of 2 functions or relations are. We sometimes elect to write a line such as the one given in \(\eqref{vectoreqn}\) in the form \[\begin{array}{ll} \left. Since \(\vec{b} \neq \vec{0}\), it follows that \(\vec{x_{2}}\neq \vec{x_{1}}.\) Then \(\vec{a}+t\vec{b}=\vec{x_{1}} + t\left( \vec{x_{2}}-\vec{x_{1}}\right)\). To see this, replace \(t\) with another parameter, say \(3s.\) Then you obtain a different vector equation for the same line because the same set of points is obtained. There is only one line here which is the familiar number line, that is \(\mathbb{R}\) itself. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Reviewed by Bogna Szyk and Jack Bowater. Legal. Free line intersection calculator. "After the incident", I started to be more careful not to trip over things. Attempt If you want to get something done, set a deadline. In other words, \[\vec{p} = \vec{p_0} + (\vec{p} - \vec{p_0})\nonumber \], Now suppose we were to add \(t(\vec{p} - \vec{p_0})\) to \(\vec{p}\) where \(t\) is some scalar. Mathepower finds out if and where they intersect. \begin{array}{c} x = x_0 + ta \\ y = y_0 + tb \\ z = z_0 + tc \end{array} \right\} & \mbox{where} \; t\in \mathbb{R} \end{array}\nonumber \], Let \(t=\frac{x-2}{3},t=\frac{y-1}{2}\) and \(t=z+3\), as given in the symmetric form of the line. This is the vector equation of \(L\) written in component form . Find a vector equation for the line which contains the point \(P_0 = \left( 1,2,0\right)\) and has direction vector \(\vec{d} = \left[ \begin{array}{c} 1 \\ 2 \\ 1 \end{array} \right]B\), We will use Definition \(\PageIndex{1}\) to write this line in the form \(\vec{p}=\vec{p_0}+t\vec{d},\; t\in \mathbb{R}\). Intersection of parabola and line. set them equal to each other. they intersect iff you can come up with values for t and v such that the equations will hold. How do I align things in the following tabular environment? Notice that in the above example we said that we found a vector equation for the line, not the equation. Last. \newcommand{\ic}{{\rm i}}% An intersection point of 2 given relations is the . This online calculator finds the equations of a straight line given by the intersection of two planes in space. Choose how the first line is given. Enter coordinates of the first and second points, and the calculator shows both parametric and symmetric line equations. We need to find the vector equation of the line of intersection. If we add \(\vec{p} - \vec{p_0}\) to the position vector \(\vec{p_0}\) for \(P_0\), the sum would be a vector with its point at \(P\). It follows that \(\vec{x}=\vec{a}+t\vec{b}\) is a line containing the two different points \(X_1\) and \(X_2\) whose position vectors are given by \(\vec{x}_1\) and \(\vec{x}_2\) respectively. Find the vector and parametric equations of a line. An online calculator to find the point of intersection of two line in 3D is presented. 4+a &= 1+4b &(1) \\ But they do not provide any examples. Conic Sections: Parabola and Focus. Calculator Guide Some theory Find the point of two lines intersection Equation of the 1st line: y = x + Equation of the 2nd line: y = x + Is it correct to use "the" before "materials used in making buildings are"? This Intersection of two parametric lines calculator provides step-by-step instructions for solving all math problems. When you've found your value for s, you can substitute it into your parametric equations for line 2. Our goal is to be able to define \(Q\) in terms of \(P\) and \(P_0\). Free line intersection calculator The first condition for a line to be tangent to a curve at a point = ( ( ) , ( ) ) is that the line and the curve intersect at that point To begin, consider the case n = 1 so we have R1 = R. There is only one line here which is the familiar number line, that is R itself. Expert teachers will give you an answer in real-time. To embed a widget in your blog's sidebar, install the Wolfram|Alpha Widget Sidebar Plugin, and copy and paste the Widget ID below into the "id" field: We appreciate your interest in Wolfram|Alpha and will be in touch soon. Get the free "Intersection points of two curves/lines" widget for your website, blog, Wordpress, Blogger, or iGoogle. A bit of theory can be found below the calculator. Work on the task that is attractive to you. Vector equations can be written as simultaneous equations. Wolfram. Conic Sections: Ellipse with Foci Let \(\vec{p}\) and \(\vec{p_0}\) be the position vectors for the points \(P\) and \(P_0\) respectively. Connect and share knowledge within a single location that is structured and easy to search. \begin{aligned} We can use the concept of vectors and points to find equations for arbitrary lines in \(\mathbb{R}^n\), although in this section the focus will be on lines in \(\mathbb{R}^3\). Suppose a line \(L\) in \(\mathbb{R}^{n}\) contains the two different points \(P\) and \(P_0\). We provide quick and easy solutions to all your homework problems. To use the calculator, enter the x and y coordinates of a center and radius of each circle. example That's why we need to check the values for $t$ and $s$ at which $x_1=x_2,y_1=y_2,z_1=z_2$. Mathepower finds out if and where they intersect. The average satisfaction rating for the company is 4.7 out of 5. (specific values unless the two lines are one and the same as they are only lines and euclid's 5th.) Once you have determined what the problem is, you can begin to work on finding the solution. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Examples Example 1 Find the points of intersection of the following lines. Calculator will generate a step-by-step explanation. Consider now points in \(\mathbb{R}^3\). This will help you better understand the problem and how to solve it. Do new devs get fired if they can't solve a certain bug? This online calculator finds and displays the point of intersection of two lines given by their equations. \end{align} They intersect each other when all their coordinates are the same. Angle Between Two Vectors Calculator. There are many ways to enhance your scholarly performance. If you're looking for an instant answer, you've come to the right place. \Downarrow \\ Point of intersection of 2 parametric lines Finding the Intersection of Two Lines The idea is to write each of the two lines in parametric form. \end {align} But they do not provide any examples. Our team of teachers is here to help you with whatever you need. Learn more about Stack Overflow the company, and our products. 9-4a=4 \\ = -B^{2}D^{2}\sin^{2}\pars{\angle\pars{\vec{B},\vec{D}}} Let \(\vec{p}\) and \(\vec{p_0}\) be the position vectors of these two points, respectively. \newcommand{\half}{{1 \over 2}}% but this is a 2D Vector equation, so it is really two equations, one in x and the other in y. If we call L1=x1,y1,z1 and L2=x2,y2,z2. \newcommand{\equalby}[1]{{#1 \atop {= \atop \vphantom{\huge A}}}}% Math problems can be frustrating, but there are ways to deal with them effectively. Enter two lines in space. find two equations for the tangent lines to the curve. A First Course in Linear Algebra (Kuttler), { "4.01:_Vectors_in_R" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.