a) Find the normal vector to the plane that passes through the points (5, 7, 0), (7, 3, 4) and (1, 3, 7) b) Use the answer to part a in order to compute the distance from the point (1, 1, 1) to the aforementioned plane.

Q: Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection…

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Q: construct a normal vector normal to the plane containing the indicated points:   P(-5,0,4)…

A: Three points are given. From these three points we can form two lines  PQ and PR These two lie on…

Q: Write down the equations of any two distinct planes with normal vector n = 〈3, 2, 1〉that do not pass…

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Q: Find a normal vector of the plane that contains the points (1, -2,0). (3, 1, 4) and (0, -1, 2).…

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Q: Find a unit normal vector to the plane passing through the points P(1, 0, 0), Q(3, 2, 0) , and R(0,…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: A normal vector for the plane through the points (2, 5, 1),(3, 7, 0), and (2, 5, 2) is _____ .

A: Given ,            (2,5,1) , (3,7,0), and (2,5,2)

Q: Find eguation of a Plane that an contains the vector: and and Z=3E

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Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

Q: 4. If (1, –1, 2) is a normal vector for the plane P, find two other normal vectors for the same…

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

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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: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

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

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Q: ) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpe ular to CD, and…

A: In this question, the concept of the dot product is applied. Dot Product The product of the…

Q: Find an equation of the plane. The plane through the point (8, 7, 1) and with normal vector 7i + j -…

A: The equation of the plane is given as:

Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

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Q: Find the vector n= normal to the plane passing through the points (0, -3, 0), (2, -1, 0) and (-2,…

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Q: Give an equation of the plane with a normal vector n = ⟨1, 1, 1⟩ that passes through the point (1,…

A: we know that equation of plane with a normal vector x0,y0,z0 and passes through point x1,y1,z1 is…

Q: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…

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Q: Find the vector in R° from point A = (x, y, z) to B = (-2, –4, 1).

A: Given points  A  = (x,y,z) B = ( -2,-4,1) To determine the vector in R3 from point A to point B

Q: Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

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Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Note: I have solved this above proof by two vector method but is not correct point for…

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: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

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Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

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: A vector orthogonal to the plane through the points (-1,0,0), (0, 1, –-2), (2, 3, 4) is O O O O

A: I have append the formula in solution part

Q: A normal vector for the plane through the points (2, 5, 1), (3, 7, 0), and (2, 5, 2) is <

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Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

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: Find a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).

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Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

Q: Find an equation of the plane. The plane through the point (4, 8, 6) and with normal vector 7i + j -…

A: Given, The plane passing through the point (4,8,6) with the normal vector 7i+j-k We know that, The…

Q: Let P be the plane through (1, 2, 3), (4, 3, 3), and (4, 4, 1). Find the vector of length 2 that is…

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Q: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).

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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: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is O O O O

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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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: 9. Use the cross product and determine the volume of the parallelepiped generated by the three…

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Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1,-2), (2,3, 4) is O O O O

A: