In $$R^3$$ 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

$$\left(0, -\frac{5}{6},-\frac{2}{3}\right)$$

B

$$\left(-\frac{1}{6},-\frac{1}{3},\frac{1}{6}\right)$$

C

$$\left(-\frac{5}{6}, 0, \frac{1}{6}\right)$$

D

$$\left(-\frac{1}{3}, 0, \frac{2}{3}\right)$$