(a) Find an equation for the line of intersection between the planes z+3y-z = 2 and 2x –y+2z = 5. (b) List and four points which lie on this line.

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

Q: Find a line equation through the point P(3,-1,4) and parallel to the line of intersection of the…

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Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

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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: 10) Find the equation of the line of the intersection of the planes 2x+3y+7z+2=D0, x+2y-3z+5=D0.

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Q: -1 and Determine an equation of the line of intersection of the planes 2x – y + 3z x + 4y – z = 2

A: I

Q: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

A:

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: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: Example 8: Find the point where the line x = 1 + t, y = 2t, and z= -3t intersects the plane…

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Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: 23. The distance of the origin from the plane 2x – 3y + 6z = 14 is A 2 В 14 C с -2 D -14

A: on solving that we get

Q: Determine the general equation of the plane 2 passing through the point P(-1,4, 5) and parallel to…

A: Follow the procedure given below.

Q: 5. (a) Find an equation for the line of intersection between the planes r+3y-z = 2 and 2x – y+2z =…

A:

Q: Find the line of intersection of the planes 3x+2y-z=7 and x-4y+2z=0.

A:

Q: 10) Find the equation of the line of the intersection of the planes 2x+3y+ 7z+23D0, x+2y-3z+ 5-0.

A:

Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = <1 , 3 , -1 >2x-y+2z=5vector b = <2 , -1 , 2 >

Q: 4) Find the equation of the line of the intersection of the planes -2x+3y+7z+2=0, x+2y-3z+5=0.

A:

Q: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

A:

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

A: To find the distance from the point 0,1,1 to the line of intersection of the planes:…

Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…

A:

Q: which of the following is the equation of the plane that is passing through the point P(2,2,-2) and…

A: Given P( 2, 2, -2) and planes  x+2y-3z=3 and x+y+z=2

Q: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

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Q: Find the equation of the plane that contains the point (4, 0, −2) and is perpendicular to the planes…

A: The equation of the plane passing through the point x0, y0, z0 is given as…

Q: (50p.) l- Find an equation of the plane through (1,3,–2) and the line of intersection of the two…

A: Given that, P1 : x-y+z=1 P2 : x+y-z=1 and Point A(1,3,-2)   We have to find Equation of Plane…

Q: Find the line of intersection of the given planes. 4x + y + z = 0 and 2x -y + 3z = 2

A: Given planes are: 4x + y + z = 0 2x - y + 3z = 0 Let us consider, z = t Then we get, 4x + y = -t 2x…

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

A: Use equation of plane

Q: Find the line of intersection of the given planes. 3x + 2y + z = ~ 1 and 2x - y + 4z = 5

A: Given: 3x+2y+z=−1                                                      ...(i)2x−y+4z=5…

Q: Find the line of intersection of the planes 2x+y-z=3 and x+2y+z=2. Find the equation of the plane…

A: Solution of part (a) in step2 and step3 and part (b) in step4.

Q: 25. Find an equation of the plane through the line of intersection of the planes x – z = 1 and y +…

A: Equation of a plane P that passes through the line of intersection of two planes P1 and P2 is given…

Q: If the image of the point (1 -2 3) in the plane 2x+3y-z=7 is the point x, y, z then the value of…

A: Let's first understand the

Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

A:

Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: Find the line of intersection of the given planes. 4x + y – z = 0 and 2x - y + 3z = 4 y = 2 + t 2

A:

Q: Find the line of intersection of the planes 2x – y + z = 2 and x + 2y – 4z = 1

A:

Q: 4) Find the equation of the line of the intersection of the planes -2xr+3y+7z+2=0, x+2y-3z+5=0.

A: We have two equations in three variables. To find the line of intersection of these planes, we fix…

Q: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

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Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

Q: Find the equation of the plane contains the line X+1/2 = Y/3 = Z-1/4 and the line of intersection of…

A: We have given the line of intersection of planes; x + 2y - 2z = 6 , 5x - 2y - z = 0 and line; X+1/2…

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Two planes are perpendicular iff their normal vectors are orthogonal

Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the…

A: consider the direction ratio of line  contaning the point ( 1, 2 ,1 )  is  l , m, n

Q: Find the symmetric equation of the line that is an intersection of the planes a: x-4y + 2z-2 = 0 and…

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Q: 2. Find the equation of the line that is parallel to the intersection of planes 12, 2x-8y + z = 0…

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Q: Find the equation of the line of intersection of the planes 2x+y-2z = 1 and x+2y-z = 4.

A: Planes are 3-dimensional spaces, that contains infinite lines. When two non-parallel planes…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

A: To find the equation of the plane passing through the point P 2,2-2 and vertical to the line of…

Q: Find the equation of the line of intersection of the planes: x+y+z=1, 2x+y-z=2

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

Q: Which of the following are symmetric equations for the line of intersection of the planes 2x+y+−6z=2…

A:

Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

A: