`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 is parallel to the plane 2x-3y+z+8=0 and which passes through the point (-1,1,2).

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

The equation of the plane parallel to the plane 2x+3y+4z+5=0 and passing through the point (1,1,1) is

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

(i) Find the equation of the plane passing through (1,-1,2) and perpendicular to the planes : 2 x + 3y - 2z = 5 , x + 2y - 3z = 8 . (ii) find the equation of the plane passing through the point (1,1,-1) and perpendicular to each of the planes : x + 2y + 3z - 7 = 0 and 2x - 3y + 4z = 0 . (iii) Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to the planes : 3x + 2y - 3z = 1 and 5x - 4y + z = 5.

Find the equation of the plane parallel to the plane 4x-3y+2z+1=0 and passing through the point (5,1,-6)