Determine if the pair of planes are parallel: (a) 4x – y + 2z=5and 7x – 3y + 4z =8 (b) x – 4y – 3z – 2=0 and 3x – 12y – 9z – 7=0

Q: Determine whether the planes 2x - 3y + 6z = 12 and 6x + 8y + 2z = 1 are parallel, orthogonal, or…

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Q: A. Find the angle between the planes x+y+z 1 and x-2y+3z 1, and Find symmetric equations for the…

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Q: The diagram approximately Illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 3x+3y+3z+1=0…

A: Given planes are,    x + y + z + 1 = 0  2x + 2y + 2z + 1 = 0  3x + 3y + 3z + 1 = 0    Thus, normals…

Q: Find the distance between these two planes x + .2y – 2z = 3 and 2x + 4y – 4z = 7 اخترأحد الخيارات a.…

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Q: Find the intersection of the planes r + 2y - 3z 1 and x -y+ z 1 two different

A: Given: equation of planes We need to find intersection of above two planes.

Q: Find the distance between the parallel planes P and P2 P: 2x-y+ 3z 6 = 0 P2: 6x - 3y+9z+ 6 = 0 8 *…

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Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-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: Find the line of intersection of the planes 3x+2y-z=7 and x-4y+2z=0.

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Q: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

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Q: Find the distance between the planes 5x - 3y + z = 9 and 5x 3y + z = -2.

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Q: Find the distance between the parallel planes: 3x - 4y + z = 12 6x - 8y + 2z = 2

A: Given, The equation of planes  3x - 4y + z = 12 6x - 8y + 2z = 2   We have to find the distance…

Q: Are the planes 2x + 4y - 2z = 1 and -3x - 6y + 3z = 10 parallel, perpendicular, or neither?

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Q: Find the distance between the planes 5x - 3y + z = 9 and 5x - 3y + z = -6.

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Q: Q8) The distance between the line x=-1+t, y3D3+2t, z=-t and the plane 2x-2y-2z=3 is: *

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Q: Find the distance between these two planes x + 2y –' 2z = 3 and 2x + 4y - 4z = 7.

A: Devide the equation of 2nd plane by 2 .we get that both planes are parallel so just apply formula…

Q: The plane containing the point (2,5,0) and parallel to the plane 3x – 7y + 6z = 8 has equation Ах +…

A: Recall:      The equation of the plane parallel to Ax+By+Cz=D and passes through the point  α,β,γ ,…

Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

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 angle (in degrees) between the planes 4y + z = 4 and – 4x + 2z= - 3.

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Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1=0 3x+3y+3z+1=0…

A: True

Q: The line L(t) = (4 – 3t, 3, 1 +t) intersects the plane 3x – 3y + 2z = -16 at the point when t =

A: To find the point of intersection of the line and the plane, substitute the values of x,y, z from…

Q: Find the value of k for which the planes: 2x-ky+4z=1 and kx+y-3z%3D2 are orthogonal.

A: we have to find the value of k for which the planes 2x-ky+4z=1 and kx+y-3z=2 are orthogonal.

Q: Find the distance between the parallel planes P1: 2x – y + 2z +6=0 and P2:6x- 3y+6z- 18 = 0

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Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: Find the distance between the parallel planes P1: 2x – y+2z + 6 = 0 and P2: 6x - 3y+ 6z – 18 = 0 3y…

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

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Q: Determine the x coordinate of the point on the plane Π:−3x−2y+2z=2 closest to the point (2,5,−5).

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Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 2x+2y+2z+2=…

A: We have to solve given problem: Concept:

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

A: Given data: Intersecting planes are, 4x-y+z-2=02x+y-2z-3=0 Point, x,y,z=-1,4,2

Q: Find the distance between the following parallel planes: (a) 3x – 4y +z=1 and 6x – 8y + 2z =3 (b) –…

A: Solve the above questions.

Q: Find the common point(s) of the planes given by II : II2 : Il : 3x + 2y – 4z = 18 y+ z= 3 Зд — 2у —…

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Q: Find the distance between the two parallel planes 2x + 4y + 12z=7 and x + 2y + 6z= 10.

A: We have to find

Q: Q:- find of the the line of interscetion plane given by 3X +6y -S2=-3 f the plane -2x + 79 -2=24

A: 3x+6y-5z+3=0 -2x+7y-z-24=0 Let z=t 3x +6y = 5t-3 -2x+7y = t+24

Q: Determine whether the planes are parallel or identical −x + 4y − z = 6, −(5/2)x + 10y − (5/2)z = 15

A: Given information: The planes are −x+4y−z=6, −52x+10y−52z=15. Calculation: The normal vectors that…

Q: Find the point of intersection for the following three planes: 3x + 4y + z + 4 =0 x + 2y + 3z +2 = 0…

A: Given Planes:

Q: he cylinder x² + y² = 2y and the plane

A: Shift cylinder at origine as centre

Q: Q3/ The distance between the plane 2x+4y-4z-22%-0 and the point(1,-2.2) will be ?

A: Basic 3d geometry problem

Q: C:- find the line of interseetion of the plane -2x +7-2=24 given by 3x +6y-52=-3 f the plane

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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: 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: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0. %3D

A: Distance between parallel planes d=(d2-d1) /(sqrt(a2+b2+c2)

Q: Find the line of intersection of the planes x + 7y + z = 9 and x − 5y + 4z = 15

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Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: Determine whether the planes are parallel, perpendicular, or neither. 2x – 10y – 8z – 1 = 0 (a) | -x…

A: Given problem:- Determine whether the planes are parallel, perpendicular, or neither.   (a) 2x…

Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: H.W 8- Find equations of the planes that are parallel to the plane x +2y- 2z= 1 and two units away…

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Q: Find the distance between the parallel planes P and P P: 2z -y+ 3z -6 =0 P: 4z - 2y + 6z - 2 =0

A: Distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is…