Find the equation of the plane through the line of intersection of the planes 
and 
, which is at a unit distance from the origin?
and 
x + 3y + 6 = 0 and 3x – y – 4z = 0
x + 3y + 6 + k(3x – y – 4z) = 0
x(1 + 3k) + y(3 – k) – 4zk + 6 = 0
Distance from origin to plane = 
36 = (1 + 3k)2 + (3 – k)2 + (4k)2
36 = 1 + 6k + 9k2 + 9 – 6k + k2 + 16k2
26 = 26k2
k2 = 1
k = 
1
case :1 k = 1
x + 3y + 6 + 1(3x – y – 4z) = 0
4x + 2y – 4z + 6 = 0
Case :2 k = – 1
x + 3y + 6 – 1(3x – y – 4z) = 0
2x – 4y – 4z – 6 = 0
10