Q8) The distance between the line x=-1+t, y=3+2t, z=-t and the plane 2x- 2y-2z=3 is: * 5 -units V12 Sunits Оз 2 -units 12 V12units O 1 jus O 4 Ja

Q: The angle between two planes is the smallest angle 0 between the planes 6x + 2y – 4z = 0 and - 7x +…

A: We will solve the problem

Q: Find the equations of planes that just touch the sphere (x – 4)² + (y – 5)² + (z – 2)² = 16 and are…

A: Sphere equation x-42+y-52+z-22=16

Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

A:

Q: For what values of Care the planes 3x+z=5 and 8x-y+Cz=9 orthogonal?

A:

Q: What is the point of intersection of the following line and plane: line: 7 = [3, 1, 2] + t [1, - 4,…

A: Given  r⇀=3,1,2+t1,-4,-8& plane π=4x+2y-z-8=0 To find point of intersection:

Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.

A:

Q: 4z: Given two lines (z++l, 5t-5,lot )f ( 34, zt+3, zt+1) located in Sicde plane, fine th plane ?

A: Equation of the plane passing through to lines can be calculated as below,

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

A:

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: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

A:

Q: 2. Find the exact value of the distance between the line of intersection of the planes 2x - y + 2z =…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 5z' + 3z gral z² - 4 plane, is

A:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 10 — 0. - - %3D -…

A:

Q: Find the distance of the point (3,8,2) from the line , -y+3 -z+2 Q2: measured parallel to the plane…

A:

Q: The lineL: x = 3 + 2t, y = 2t, z = tintersects the plane x + 3y - z = -4 in a point P. Find the…

A:

Q: Find the distance between the planes 3x-y+6z=7 and -6x+2y-12z=1. Round off answer to four decimal…

A: Given: To explain the correct option of the given statement as follows, The given planes are 3x-y+6z…

Q: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

A:

Q: 14) Determine the distance between the parallel planes: 6z = 4y – 2x; and 9z = 1 – 3x + 6y.

A: Given:-planesP1: 6z=4y-2x2x-4y+6z=0x-2y+3z=0P2: 9z=1-3x+6y3x-6y+9z=1x-2y+3z=13To find : distance…

Q: The distance between the point ( 9,8,3) and the plane x + y – 2z = 5 is .... %3D

A:

Q: Find the distance between the parallel planes.2x + y - 2z = 0 and 2x + y - 2z = 5

A: The given parallel planes are 2x+y-2z=0  and  2x+y-2z=5. The objective is to find the distance…

Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

A:

Q: Find a plane containing the point (- 5, – 5, 2) and the line r (t) = (1, – 2, 1) + t(4, 7, 5).

A: Given that the required plane passes through the point P=(-5,-5,2) and required plane contains the…

Q: int at which the line ⟨4,−1,−5⟩+t⟨−3,3,2⟩⟨4,−1,−5⟩+t⟨−3,3,2⟩ intersects the plane…

A: Given the line 4,-1,-5+t-3,3,2  intersects the plane -x+y+z=18.

Q: 2. Obtain an equation for a plane 7 that includes straight line(2"--5) and point(-2,1,1).

A:

Q: Find the point at which the line intersects the given plane: 5x = y/2 = z + 2 and 10x - 7y + 3z +…

A:

Q: Find the distance between the point (2, 8, 4) and the plane 2x + y + z = 5.

A: we have to find the distance between the point (2,8,4) and the plane 2x+y+z=5. as we know that the…

Q: find distance between plane(6x_2y_z+4=0)and point (3,2,1) P 3:08

A: Given,           The plane is 6x-2y-x+4=0 and the point is 3,2,1.

Q: Derermine the pointof intersection of the linel:- [-6,9,-1]+t[-a,3 ,1], t ER, and the plane, TT-x +…

A:

Q: Q1/: Find the distance between plane (6x - 2y - z +4 = 0) and point (3, 2, 1). (6 marks)

A:

Q: Find the distance between the given parallel planes. 2x - 3y + z = 8, 4x - 6y + 2z = 1

A: The solution are next step

Q: Determine the distance from point Q = (2, 6, 9) to the plane x + 2y + 2z = 8

A:

Q: Find the distance from the point Q(6, -2, 4) to the plane 2x - y + 2z = 4.

A: It is given that a point Q6,-2,4 and equation of the plane 2x-y+2z=4. Here, x1=6, y1=-2, z1=4  and…

Q: Find the distance between the parallel planes −3x+y+2z=−4 and 6x−2y−4z=1?

A:

Q: Find the distance from the point (5, -4, 1) to the plane −3x−2y−3z=−4

A:

Q: Find the distance between the given parallel planes. 2x - 4y + z = 8, 4x - 8y + 2z = 3

A:

Q: What is the distance between the point A(1,-1,3) and the plane x + 2y + 2z + 1=0 ?

A: To find The diatance between the point A(1,-1,3) and the given plane

Q: 14) Determine the distance between the parallel planes: 6z = 4y - 2x; and 9z = 1- 3x + 6y.

A: Given problem:- Determine the distance between the parallel planes: 6z = 4y - 2x and 9z = 1 - 3x +…

Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.

A:

Q: Find angle between two planes given by 2x + y – z = 29 and 3x + y + 2z = 6. %3|

A: we have to find the angle between the two planes given by 2x+y-z=29 and 3x+y+2z=6. the equations of…

Q: Find the point at which the line (0, –3, 5) + t(4, –1,2) intersects the plane 4x + 4y – 4z = 0.

A:

Q: Pind all point on 2=8-3x°- 243 where ohe bonyent plane is orehogonal :2-36,リ=タ +&e, 2-5-ビ to the…

A:

Q: between the point and the plane. 43. (1,−2, 3); 2x − 2y + z = 4

A: Given: The point is 1,-2, 3 and the equation of the plane is 2x-2y+z=4 To find the distance between…

Q: Determine the distance from point P(-2, –1, 1) to the plane [x, y, z] = [4, –1, 6] + t[1, 6, 3] +…

A: Parametric equation of a plane is: x,y, z=p+at+bs where a and b are the vectors parallel to the…

Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

Q: Find the distance between the point (3, -4, 2) and the plane 5x- 2y +z = 10.

A:

Q: Find a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

A:

Q: Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x - 6y + 2z = 5

A:

Q: The distance from the point S(-7, 8, -4) to the plane 10x+2y+11z=2. 20 3 8 15 8 225

A: The equation of the plane is  10x+2y+11z = 2 The point is S-7,8,-4 To evaluate : The distance from…

Q: Are the plane 2x-y-4z 10 and the line {x = 2+4t,y 5- 2t,z =-8t} parallel or orthogonal?

A: We have to find out