x − 3y + 6z = 4 e 5x + y − z = 4

Q: Consider the planes given by the equations x + 2y + 3z = 4 3x + 4y + 5z = 2 5x + 4y + (k - 1)z = k –…

A: This is a non homogeneous system AX=b Concepts required : Infinite solution of the system AX=b will…

Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

Q: Find the distance from the point (7, -14, -21) to the plane:  2x - 3y - 6z = 1

A:

Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with…

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: Determine the angle between the following two pl -x+6y + 3z - 6 = 0 2x +3z- 10 = 0

A: Formula for the angle between two planes  A1x+B1y+C1z=D1andA2x+B2y+C2z=D2 is…

Q: Find the angle of intersection of the plane 4x - 2y - 2z = 4 with the plane -1x + 3y + 2z = -5.…

A: We know angle of intersection between two planes  A1x+B1y+C1z=D1 and A2x+B2y+C2z=D2 is…

Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z 3 -12…

A: The point of intersection will satisfy the line as well as the Planes equation.

Q: Given 2 lines expressed in terms of vectors, how to determine the normal vector on the intersection…

A:

Q: Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A:

Q: Find the equation of the XZ plane.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Determine parametric equations of the line of intersection of the planes x+2y+3z=4 and -2x+z=0. Then…

A: Let us consider two planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0  Intersection of two planes is line…

Q: calculate the distance between the point P (2, 3) and the point Q (1,-2) 20 3 us O V25 4 jus O V26

A: The distance between two points (x1, y1) and (x2, y2) is                    d=(x2-x1)2+(y2-y1)2…

Q: 7x + 3y + 4z = 5, and 21x + 9y +12z = 13

A:

Q: Draw and label a plane Q for each relationship. 6. AB is in plane Q 7. ST intersects AB at P. 8.…

A:

Q: Do three points determine a plane?

A: We know by following ways plane can be determined: 1. Three non collinear points determine the…

Q: Describe the plane x = 4.

A: Given, plane x=4we have to describe the plane x=4

Q: u = 57 - 5] + k and 7 = 27 + 14k.

A:

Q: he intercepts of the plane given by

A: Intercepts of the plane are (3,5,3).

Q: If not, find a parametric equation of the line of intersection of the two planes. Find, correct to…

A: