A plane which is perpendicular to two planes `2x-2y+z=0 and x-y+2z = 4` passes through `(1, -2, 1)`. The distance of the plane from the point (1, 2, 2) is

A plane which prependicular totwo planes 2x-2y+z=0 and x-y+2z=4 passes through the point (1,-2,1) is:

A plane passes through (1,-2,1) and is perpendicualr to two planes 2x-2y+z=0" and "x-y+2z=4, then the distance of the plane from the point (1,2,2) is

Find the distance of the plane 2x-y+2z+1=0 from the origin.

Find the equation of the plane passing through the point A(1,2,1) and perpendicular to the line joining the points P(1,4,2) and Q (2,3,5) . Also , find the distance of this plane from the line (x+3)/(2)=(y-5)/(-1)=(z-7)/(-1) .

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

Prove that the equation of the plane which is pendicular to the plane 3x+2y+6z+4=0 is 2x-6y+z=0 .

Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=5 and a t a distance of 1/sqrt6 from the point (2,1,-1).

Equation of a line in the plane pi =2x-y+z-4=0 which is perpendicular to the line l whose equation is (x-2)/1=(y-2)/(-1)=(z-3)/(-2) and which passes through the point of intersection of l and pi is (A) (x-2)/1=(y-1)/5=(z-1)/(-1) (B) (x-1)/3=(y-3)/5=(z-5)/(-1) (C) (x+2)/2=(y+1)/(-1)=(z+1)/1 (D) (x-2)/2=(y-1)/(-1)=(z-1)/1

For the line (x-1)/1=(y-2)/2=(z-3)/3, which one of the following is correct? a. it lies in the plane x-2y+z=0 b. it is same as line x/1=y/2=z/3 c. it passes through (2,3,5) d. it is parallel t the plane x-2y+z-6=0

let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P_1 : x + 2y-z +1 = 0 and P_2 : 2x-y + z-1 = 0 , Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P_1 . Which of the following points lie(s) on M? (a) (0, - (5)/(6), - (2)/(3)) (b) (-(1)/(6), - (1)/(3), (1)/(6)) (c) (- (5)/(6), 0, (1)/(6)) (d) (-(1)/(3), 0, (2)/(3))