Foot of the perpendicular form (-2,1,4) to a plane `pi` is (3,1,2). Then the equation of theplane `pi` is (A) `4x-2y=11` (B) `5x-2y=10` (C) `5x-2z=11` (D) `5x+2z=11`

A plane through the line (x-1)/1=(y+1)/(-2)=z/1 has the equation (A) x+y+z=0 (B) 3x+2y-z=1 (C) 4x+y-2z=3 (D) 3x+2y+z=0

Equation of the plane containing the straighat line x/2=y/3=z/4 and perpendicular to the lane containing the straighat lines x/3=y/4=z/2 and x/4=y/2=z/3 is (A) x+2y-2z=0 (B) 3x+2y-2z=0 (C) x-2y+z=0 (D) 5x+2y-4z=0

Let the equations of two planes be P_1: 2x-y+z=2 and P_2: x+2y-z=3 Equation of the plane which passes through the point (-1,3,2) and is perpendicular to each of the plane P_1 and P_2 is (A) x-3y-5z+20=0 (B) x+3y+5z-18=0 (C) x-3y-5z=0 (D) x+3y-5z=0

The equation of the plane through the point (1,2,-3) which is parallel to the plane 3x-5y+2z=11 is given by (A) 3x-5y+2z-13=0 (B) 5x-3y+2z+13=0 (C) 3x-2y+5z+13=0 (D) 3x-5y+2z+13=0

A plane which passes through the point (3,2,0) nd the line (x-4)/1=(y-7)/5=(z-4)/4 is (A) x-y+z=1 (B) x+y+z=5 (C) x+2y-z=1 (D) 2x-y+z=5

(a) Find the foot of the perpendicular from the point (i) (2, -1,5) on the line : (x -11)/(10) = (y + 2)/(-5) = (z + 8)/(11) (ii) (0,2,3) on the line (x +3)/(5) = (y-1)/(2) = (z + 4)/(3) . (b) Also, find the length of perpendicular in part (ii).

Find the length and the foot of the perpendicular drawn from the point (2,-1,5) to the line (x-11)/(10)=(y+2)/(-4)=(x+8)/(11)

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

Solve the system of equations by cramer's rule: 5x-y+4z=5 , 2x+3y+5z=2 , 5x-2y+6z=-1