Answer is (A) 1/3√2
Given:
First two planes: 2x - 2y 3z - 2 = 0, x - y + z + 1 = 0
Equation of plane that passes through the line of intersection of the first two planes is
2x - 2y + 3z - 2 + λ(x - y + z + 1) = 0
x(λ + 2) - y(2 + λ) + z(λ + 3) + (λ - 2) = 0 (1)
Equation (1) should have infinite number of solutions with the last two given planes, that is
x + 2y – z – 3 = 0
3x – y + 2z – 1 = 0
Therefore,
On solving, we get λ = 5.
Substituting this value of v in Eq. (1), we get
7x - 7y + 8z + 3 = 0
Therefore, the perpendicular distance from the origin (0, 0, 0) of the plane is
3/√167 = 1/3√2