Find the distance between the point (3, 1, −2) and the plane x + 2y − 2z = 4.

Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

A:

Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

A:

Q: Find the distance from the origin to the plane 2 = z - x.

A: Given point is (0,0,0) Given plane is 2=z-x or x-z+2=0

Q: Find the distance between the point and the plane.

A: The distance of a point from a plane in the standard equation form is equal to . The given point…

Q: Find the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

A:

Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

A: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

Q: Find the distance from the point (−3,0,2) to the plane - 3x + y + 5z = 0

A:

Q: Find the point in the plane 2x − y + 4z = 16 that is closest to the origin.

A: Given:     Plane 2x-y+4z=16 Distance of point P(x1,y1,z1) from plane Ax+By+Cz=D is…

Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

A:

Q: Find the distance from the line x = 2 + t, y = 1 + t, z = -(1/2) - (1/2)t to the plane x + 2y + 6z =…

A:

Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (3,-3,2)…

A:

Q: I need the answer as soon as possible

A:

Q: find the distance from the point to the plane. (0, -1, 0), 2x + y + 2z = 4

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2 - 2t meets the plane 6x + 3y – 4z = -12

A: Given line is x = 2, y = 3 + 2t z = -2-2t and the plane 6x + 3y - 4z = -12

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

A:

Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

A:

Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

A:

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

A:

Q: Find the distance from the point (2, 0, 0) to the plane x + 2y + 2z = 0.

A: Given a point, (2, 0, 0) and the equation of the plane x + 2y + 2z = 0.

Q: The plane 6x + 8y + 60z = 700 intersects th of the highest and lowest points or coordinates

A: Given that the plane           6x+8y+60z=700  and the cone                            z2=x2+y2

Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

A:

Q: find the distance from the point to the plane. (1, 0, -1), -4x + y + z = 4

A: Concept -Let the equation of plane be -Ax+By+Cz+D = 0And the coordinates of a point be - (x1, y1,…

Q: 4. Write the equation of the plane parallel to the z-axis, with xy-trace x + y - 2 = 0.

A: Write the equation of the plane parallel to z axis, with xy trace x+y-2=0.

Q: The distance from the point P(1,2,3) to the plane x +y + z = 0 is

A:

Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

A:

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 7z + 13 =…

A:

Q: Find the distance from the line x = 2 + 1, y = 1 + 1, z = -(1/2) – (1/2)t to the plane x + 2y + 6z =…

A: The equation of line: x=2+t,  y=1+t,  z=-12-12tTherefore:x-21=y-11=z+12-12 Equation of the plane is:…

Q: Find the point of intersection of the line x = 2 − 3t y = 4 + 2t −∞ < t < ∞, z = 3 − 5t, and…

A: x=2-3ty=4+2tz=3-5tand the plane 2x+3y+4z+8=0

Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z=12

A: As there are multiple questions, the first one (19) is solved here.

Q: Find the point on the plane x - 2y + 3z = 12 that is closest to the point (0, 2, 2). (x, y, z) =

A: Just I have used the Lagrange multipliers method and find the required solution.…

Q: Find the distance from the point (1, 1, 1) to the plane 2x + 2y + z = 0.

A:

Q: find an equation for the plane that is tangent to z=4x^2+y^2 at the point (1,1,5)

A:

Q: Find the distance between the point P(1, -2, -3) and the plane x + 2y + 2z - 15 = 0. Answer:

A:

Q: Find the distance between the point and the plane. (0, 0, 0) 2x + 6y + z = 12

A:

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: Find the distance from the line x = 2 + t, y = -2+ 2t, z = 4 – t and the plane 2x – 3y – 4z = 12…

A:

Q: Find a plane that is perpendicular to the two planes x + y = 3 andX + 2y - Z = 4.

A: Since we have been given two planes x+y=3-(i) and x+2y-z=4-(ii)Our Aim is to find a plane that is…

Q: Find an equation for the plane tangent to the surface z = 2x2 - 7y at the point (3,-1,5)

A: Given surface z=2x2-7y and the point 3,-1,5. The main objective is to find an equation for the plane…

Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

A:

Q: A) Find the point at which the line x = 2, y = 3+2t, z = -2- 2t meets the plane 6x + 3y - 4z = -12

A: The line is given by:x=2, y=3+2t, z=-2-2tand the plane is given by6x+3y-4z=-12.We need to find the…

Q: Find the point closest to the origin on the curve of intersection of the plane 2y + 4z = 5 and the…

A: We have to find the point closest to the origin on the curve of the intersection of the plane…

Q: Q2) Find the distance from the point P (1, 2, 3) to the plane x-3y + 2z= 4.

A:

Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: Find the point on the plane x+y+z%3D24 that is closest to the point (1,1,1).

A:

Q: Find the point on the plane x – 3 y – 2 z = 14 that is closest to the point (0, 3, 3) .

A: We have the plane x-3y-2z=14 The normal vector to a plane ax+by+cz=d is a,b,c Hence, the normal…

Q: Find the distance between the origin and the intersection line of the planes : 2x+y+z=2 and x+2y+z=3…

A:

Q: Find the distance from the point B = (1,0, 2) to the plane 2P whose general equation isx + y - z =…

A: Given: equation of plane is x+y-z=1  We know that distanced from the pointx1,y1,z1 to the…

Q: Find the distance from the point Q to the plane p. Q= (0, 0, 0), p with equation x - 2y + 2z = 1

A: GivenQ=0,0,0p:x−2y+2z=1

Q: Find the equation of the plane in the form z = c + mx + my containing the line in the xy-plane where…

A: Plane