Question

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 :

• A. 16
• B. 28
• C. 10
• D. 22

Answer 1

Answer: (B)

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 $28$