Projection of a Line Segment on a Line

Q. Three planes $P_1:2x+y+z-1=0,$ $P_2:x-y+z-2=0$ and $P_3:\alpha x-y+3z-5=0$ intersect each other at point $P$ on $XOY$ plane and at point $Q$ on $YOZ$ plane, where $O$ is the origin. Then which of the following statements is (are) CORRECT?

1. The value of $\alpha$ is $4$
2. Straight line perpendicular to plane $P_3$ and passing through $P$ is $\frac{x-1}{4}=\frac{y+1}{-1}=\frac{z}{3}$
3. The length of projection of $\overrightarrow{PQ}$ on $x$-axis is $1.$
4. Centroid of the triangle $OPQ$ is $(\frac{1}{3},\frac{-1}{2},\frac{1}{2})$

Q. Find the projection of line joining (1, 2, 3) & (-1, 4, 2) on the line having direction ratios (2, 3 , -6) .

1. $\frac{8}{7}$
2. $\frac{7}{8}$
3. $\frac{6}{5}$
4. $\frac{5}{6}$