Find an equation of the plane containing the points (0, 1, 0), (2, 1, 1) and (-1,3,0). O A. The three given points are collinear. They do not span a plane. О В. 2х + у — 42 + 1 — 0 С. 2х + у — 423D 1 O D. Зх +у — 62 — 1 O E. 2x + y+ 4z = 1

Q: Find an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

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Q: Find the equation of the plane through the point (2,4,3)(2,4,3) that is perpendicular to the line…

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Q: Find an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t)=…

A: A detailed solution is given below

Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

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Q: Which of the following is the equation of the plane where x-2y + 32 = 3 and x+y+z=2 and passes from…

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Q: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: Find the equation for the plane through Po(7.- 3. - 1) perpendicular to the following line. x=7+t,…

A: Ans     equation  of  line          x=7+t,   y=-3-3t,  z=-2t  or   x-71=y+3-3=z+0-2

Q: A linear combination of of u = 3 and v= 4 will give a plane in R³. Given that the point (2, 1, −1)…

A: Consider the given linear combination, u=132 and v=-144 will give a plane in ℝ3. The equation of a…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: The equation of the plane passing through the point A(8, 10, 9) and orthogonal to the line x = 7+…

A: Given: Point A(8,10,9) Line x=7+8t , y=6+4t , z=5+9t

Q: The equation of the plane passing through the point A(6, 6, 6) and orthogonal to the line a = 11 +…

A: The objective is to find the equation of the plane passing through the point A6,6,6 and orthogonal…

Q: Find an equation of a plane that passes through the points P(4,2,1), Q(-1,-2,2), R(3,1,-2) a.…

A: A plane that passes through the points P(4,2,1), Q(-1,-2,2), R(3,1,-2)

Q: Find an equation of the form ar+by+cz = d for the plane that passes through the points A(3,2,0),…

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Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

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Q: Determine the equation of the plane passing through the points P(-2, 1, 5) and Q(4,9, -3) and R(3,…

A: To determine the equation of the plane passing through the points P(-2, 1, 5) and Q(4, 9, -3), and…

Q: Find an equation for the plane parallel to – 2x + 9y – 2z 30 and containing the point (1, 4, 3)

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Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

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Q: Write the equation for the plane. The plane through the point P(3, - 4,5) and normal to n= (5,5,5) O…

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Q: Find an equation for the plane parallel to the liner =1- 21, y = 2 + 3t %3D 2 = 1+ 2t and that…

A: Given: Plane is parallel to the line x=1-2ty=2+3tz=1+2t Also, the plane contains the line of…

Q: Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the…

A: Topic = Vector correct answer e

Q: Which of the following equations define the plane passing through the points (3,0, 0), (0, –7,0),…

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Q: Find the equation of the plane having the points P(1, 2,5), Q(-2, 0, 1), and R(-3,-4,1). 8x + 2y 5z…

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Q: Find an equation of the plane containing the points P(O,0,o) and Q(2,2,2) and parallel the line…

A: Given:- Equation of line x= t, y = 1,z= t  To find:- An equation of the plane containing the points…

Q: Find an equation of the plane. The plane that passes through (7, 0, –4) and contains the line x = 4…

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Q: Find an equation of the plane through (-8, 6, - 6) that is perpendicular to the planes 9x - y + z =…

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Q: Find the intersection of the line r(t) = (2, 1, 3) + t(3, -3, 1) and the plane 4x - 4y - 2z = 6.

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

Q: The equation of the plane passing through the point A(6, 6, 6) and orthogonal to the line a 11+7t, y…

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Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

Q: 1. Find the equation of the plane that passes through the points P(2,0,1), Q(1,0,-1) and R(3,0,1).

A: We have, Vectors in the plane are, Therefore, equation of plane passes through 3 points will be,…

Q: 5. Find the Cartesian equation of the plane that has a z-intercept of 3, a y-intercept of -2, and is…

A: Explained below

Q: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

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Q: Which of the following is the equation of the plane containing the points (2,1,2), (4,1,0) and (5,0,…

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Q: 2. Find an equation of the plane determined by the points P(1,1,0), Q(1,0,1) and R(0, 1, 1).

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Q: Find the equation of the plane contains the line x=3t,y=1+t, z=2t, and parallel to the line of…

A: Given, the plane contains the lines x = 3t, y = 1 + t, z = 2t and parallel to the line of…

Q: 5. Find the equation of the plane that passes through the point (6,0,-2) and contains the line X =…

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Q: Determine the equation of the plane that contains the points P=(1,-2,0) P=(1,-2,0), Q=(3,1,4)…

A: Here we have to determine the equation of the plane that contains the points P(1,-2,0), Q(3,1,4) and…

Q: A linear combination of of u 3 and v= A on the plane, which one of the following is the equation of…

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Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is  x+2y-10z+12=0 We need to find the equation of plane that is…

Q: Find an equation of a plane containing the line r (5, 5, 4) + t(7, -10, 5) which is parallel to the…

A: Equation of the plane containing the line given by: r=5i+5j+4k+t7i-10j+5k and parallel to plane…

Q: Find an equation of the plane that contains the point (2,0,-8) and contains the line y- 2 z+1 x +4 =…

A: The plane passes through the point 2, 0, -8. Thus, the equation of the plane can be written as…

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

A: Calculus Question

Q: Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the…

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Q: of the

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Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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Q: Which of the following planes is the equation for the plane with an x-intercept at P(2,0,0), a…

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