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Q.
If the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{1}$ and $\frac{x-a}{2}=\frac{y+2}{3}=\frac{z-3}{1}$ intersects at the point $P$, then the distance of the point $P$ from the plane $z = a$ is :
Point on $L _1 \equiv(\lambda+1,2 \lambda+2, \lambda-3)$
Point on $L _2 \equiv(2 \mu+ a , 3 \mu-2, \mu+3)$
$\lambda-3=\mu+3 \Rightarrow \lambda=\mu+6$...(1)
$2 \lambda+2=3 \mu-2 \Rightarrow 2 \lambda=3 \mu-4$...(2)
Solving, (1) and (2)
$\Rightarrow \lambda=22 \& \mu=16 $
$\Rightarrow P \equiv(23,46,19)$
$\Rightarrow a =-9$
Distance of $P$ from $z =-9$ is $28$