Let M be a plane with the following properties: • M contains the point with coordinates (1,-2,-1) (€) 2. • M is orthogonal to the vector 0 What is the distance of the point with coordinates (-1, 1, -1) from M? [Please enter your answer numerically. You will be marked correct as long as what you enter is within 0.5 of the correct answer.]

Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…

Q: Let ū = (0, 1, –1), v = (2, 1,0) and w = (4, 1, 1). a) Show that ū, ū and w lie in the same plane…

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Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

Q: 4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R…

A: This is a problem of Vector Algebra.

Q: Let M be a plane with the following properties: • M contains the point with coordinates (0,0,1) • M…

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = Q =…

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Q: 10) Eind the eçuation of the plane Contaihins the two vectors 2and ,and the point PU2ー)

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Q: 5) Consider the vector ū = (1,2, –2) and the points Q(5, 5, 2) and R(3, 0,0). 5.1) Find the equation…

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Q: a) Explain fully, atleast three possible relationships between two lines in R3 [c3] b) Which of the…

A: (a) The relationship between any two lines in ℝ3 is always one of the following three: They can be…

Q: Let M be a plane with the following properties: • M contains the point with coordinates (1,1,-1) ()…

A: since plane is passing through the point (1,1,-1) and orthogonal to the vector 200

Q: 1. Let P(1, 1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the plane…

A: You are asked multiple questions. As per our guideline we can solve only one. Please repost the rest…

Q: If a plane is parallel to one of the coordinate planes, then its normal vector is parallel to one of…

A: We will solve the problem

Q: 7) Find a vector that is orthogonal to the plane that contains the points P(1,–2,4), Q(-2,3,2), and…

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Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P=(2,0,-4),…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (0,2,0) •…

A: By the help of formulaes we solve the given question as follows:

Q: 1. Find an equation of the plane containing the point P(3,2,7) and having a nor- mal vector i = (2,…

A: Given: Point on the plane:  A=(3, 2, 7)Normal vector to the plane is:  n→=2, 5, 2

Q: Let M be a plane with the following properties: • M contains the point with coordinates (1,1,0) 2 •…

A: Consider the given information:

Q: 4-) Find the a Cute augle between the liue joning the two Points AC42,3),B(5,1,7) , and the Plane…

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Q: Consider the triangle in 3-space whose vertices are the points P(1, 1, 1), Q(5, -10, 2), and R(7,…

A: ∴QP→ = (-4i^ + 11j^ - k^)QR→ = 2i^ + 9j^ + ok^Now for a vector which is prependiculor to plane of…

Q: 4-) Find the a Cute augle between the liue joning the two Points ACY2,3),B(5,1,7) , and the Plane…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (1,1,-1) ()…

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Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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Q: Q1-)A-) Find the distance from the point (0,1,1) to the line of intersection of the planes : x + 2y…

A: Given: A) Point (0, 1, 1) and the planes x + 2y + z = 1, x - y + 2z = -8. B) Vertices of triangle…

Q: 2- A plane is defined by any three points that are in the plane. If a plane contains the points…

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Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

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Q: Given points P = (2,1,5), Q = (-1,3,4), R = (3,0,6), af Find the unit vector orthogonat…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (-1,1,0) • M…

A: Solution      Plane M contains the point -1,1,0      M is orthogonal to vector 200…

Q: Let M be a plane with the following properties: • M contains the point with coordinates (-1,-1,0) •…

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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: Determine any three points on the plane given by 5x - 6y + 10z - 15  = 0. Using these points, give a…

A: The given plane is: 5x - 6y + 10z - 15  = 0. We have to find any three points on the plane. Using…

Q: Let M be a plane with the following properties: M contains the point with coordinates (2,-2,1) () •…

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Q: 1 Which vector is perpendicular to the plane -2x + 3y – 4z = 9? 1 1 2' 3 О 2, -3,4] 2 1 9 3? О 12,3,…

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Q: a)Find the equation of the plane in 3- dimensional space passing through the points P = (1, 2, 1), Q…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 5) Consider the vector ū = (1,2, –2) and the points Q(5, 5, 2) and R(3,0,0). Answer the following…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Let b = 4i + 3j and c be two %3D vectors perpendicular to each other in the xy-plane. All vectors in…

A: Given: b→=4i+3j and c→ are two vectors perpendicular to each other in xy-plane.  To find: All the…

Q: Find a vector that is orthogonal to the plane containing the points P = (3,0, 1), Q = (4, –2, 1) and…

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Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1). Find…

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Q: Find a parametric representation for the plane that passes through the point (2, –3, 4) and contains…

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Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

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Q: 5) Consider the vector ū = (1,2, –2) and the points Q(6, 5, 2) and R(3,0, 0). Answer the following…

A: Plane and vector

Q: Find an equation of the plane that passes through the point P and has the vector n as a normal. ■ 3.…

A: An equation of the plane that passes through the point P and has the vector n as a normal3.…

Q: Let P(1,1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the plane containing…

A: Given problem:- Let P(1,1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the…

Q: Suppose vectors u and v lie in the xy-plane (the z-component of each vector is zero). Now suppose…

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Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: Suppose that u = (0, b) is a non-zero vector in R?. Show that the line L = Span({ủ}) has Cartesian…

A: Consider the given information.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.