JEE 2023 — Mathematics PYQ

Solving:

Line ki equation: $\frac{x+3}{3}=\frac{y-2}{3}=\frac{z-3}{-1}=\lambda$

Line par generic point $Q$: $(3\lambda -3,3\lambda +2,-\lambda +3)$

Perpendicular condition se: $\lambda =2$

Foot of perpendicular $Q$: $(3,8,1)$

Distance $PQ=\sqrt{(4-3{)}^2+(6-8{)}^2+(-2-1{)}^2}=\sqrt{1+4+9}=\sqrt{14}$

Sahi Option: (1)