If the equation of perpendicular from origin to the line x + 4y +4z - 27 = 0 = 2x + 2y + 5z -21 is y - mx = 0 = z - nx then 2n - m =

In the following cases, find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane : (i) 2x + 3y + 4z - 12 = 0 (ii) 3y + 4z - 6 = 0 (iii) x + y + z = 1 (iv) 5y + 8 = 0.

(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.

The symmetric form of the equation of the line x + y-z =3, 2x+3y+ z+4=0 is :

Prove that the lines 3x + 2y + z – 5 = 0 = x + y – 2z – 3 and 2x – y – z = 0 = 7x + 10y – 8z – 15 are perpendicular

Solve the following equations by reduction method : x - y + z = 4, 2x + y - 3z = 0 , x + y + z = 2

Find the equation to the straight line drawn from the origin to intersect the lines 3x+2y+4z-5=0=2x-3y+4z+1 and 2x-4y+z+6-0=3x-4y+z

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin. (a) 2x" "+" "3y" "+" "4z" "" "12" "=" "0 (b) 3y" "+" "4z" "" "6" "=" "0 (c) x" "+" "y" "+" "z" "=" "1 (d) 5y" "+" "8" "=" "0

Projection of the line x+y+z-3=0=2x+3y+4z-6 on the plane z=0 is