Consider the lines

$l_1$:$,x=1+2t,y=1-t,z=3t,$tinR,

$l_2$:$,\frac{x-1}{2}=\frac{y+2}{-1}=z-5,$

the plane

$$ : $,x+2y+3z+3=0,$

and the point $P(1,0,2).$

$($a$)$ Find the point $Q$ of intersection of line $l_2$ and the plane $.$

$($b$)$ Either find an equation of the plane which is perpendicular to the plane $$ and passes through the points $P$ and $Q,$ or explain why such a plane does not exist.

$($c$)$ Do the lines $l_1$ and $l_2$ intersect each other? If so$,$ find the point of their intersection.

$($d$)$ Are the lines $l_1$ and $l_2$ parallel to each other? Explain.

$($e$)$ Either find an equation of the plane containing the line $l_1$ that is also parallel to the line $l_2,$ or explain why such a plane does not exist.

$($f$)$ Either find an equation of the plane containing the line $l_1$ that is also perpendicular to the line $l_2,$ or explain why such a plane does not exist.

$($g$)$ Find both parametric and symmetric equations $($if possible$)$ for all lines which are parallel to the plane $$ and pass through the point $P.$