In R³, 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 $P_1:2x-y+z-1=0$. Let M be the locus of the feet of the perpendicular drawn from the points on L to the plane P₁. Which of the following points lie(s) on M?

Line L will be parallel to the line of intersection of P₁ and P₂ a,b,c are the dr's of line L.

$a+2b-c=0, 2a-b+c=0$

$a:b:c=1:-3:-5$

‘L’ is $\frac{x-0}{1}=\frac{y-0}{-3}=\frac{z-0}{-5}$

foot of the perpendicular from origin to the plane P₁ is $\left(-\frac{{\displaystyle 1}}{{\displaystyle 6}},\frac{{\displaystyle -1}}{{\displaystyle 3}},\frac{{\displaystyle 1}}{{\displaystyle 6}}\right)$

equation of projection of the line L on plane P₁, is $\frac{x+\frac{1}{6}}{1}=\frac{y+\frac{2}{6}}{-3}=\frac{z-\frac{1}{6}}{-5}=k$

$\left(0,-\frac{{\displaystyle 5}}{{\displaystyle 6}},\frac{{\displaystyle -2}}{{\displaystyle 3}}\right) \left(\frac{{\displaystyle -1}}{{\displaystyle 6}},\frac{{\displaystyle -1}}{{\displaystyle 3}},\frac{{\displaystyle 1}}{{\displaystyle 6}}\right)$ satisfy M