`P(2,1,2),Q(1,2,1)` are two points on a plane which is parallel to the line `2x=3y,z=1`. Find the equation of the plane.

Find the equation of a plane which is parallel to the plane x-2y+2z=5 and whose distance from thepoint (1,2,3) is 1.

Find the equation of the plane which passes through the point (3,4,-1) and is parallel to the plane 2x-3y+5z+7=0. Also, find the distance between the two planes.

Find the equation of the plane which is parallel to 2x-3y+z=0 and which passes through (1, -1, 2).

Let P be the image of the point (3, 1, 7) with respect to the plane x-y+z=3 . Then, the equation of the plane passing through P and containing the straight line (x)/(1)=(y)/(2)=(z)/(1) is

Find the equations of the planes parallel to the plane x-2y+2z-3=0 which is at a unit distance from the point (1,2,3) .

Find an equation or the line that passes through the point P(2,\ 3,\ 1) and is parallel to the line of intersection o the planes x+2y-3z=4\ a n d\ x-2y+z=0 .

Find the equation of the plane passes through the point (1,-3,1) and parallel to the plane 2x+3y+z=1 .

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0 . Then find the distance of plane thus obtained from the point A(1,3,6) .

Let a plane pass through origin and be parallel to the line (x-1)/2=(y+3)/-1=(z+1)/-2 is such that distance between the plane and the line is 5/3 . Then equation of the plane is/are

Let two planes p _(1): 2x -y + z =2 and p _(2) : x + 2y - z=3 are given : Equation of the plane which passes through the point (-1,3,2) and is perpendicular to each of the plane is: