jee-advanced 2008 Q18

jee-advanced · India · paper2 Vectors 3D & Lines Shortest Distance Between Two Lines
Consider the lines
$$\begin{aligned} & L _ { 1 } : \frac { x + 1 } { 3 } = \frac { y + 2 } { 1 } = \frac { z + 1 } { 2 } \\ & L _ { 2 } : \frac { x - 2 } { 1 } = \frac { y + 2 } { 2 } = \frac { z - 3 } { 3 } \end{aligned}$$
The shortest distance between $L _ { 1 }$ and $L _ { 2 }$ is
(A) 0
(B) $\frac { 17 } { \sqrt { 3 } }$
(C) $\frac { 41 } { 5 \sqrt { 3 } }$
(D) $\frac { 17 } { 5 \sqrt { 3 } }$
Consider the lines

$$\begin{aligned}
& L _ { 1 } : \frac { x + 1 } { 3 } = \frac { y + 2 } { 1 } = \frac { z + 1 } { 2 } \\
& L _ { 2 } : \frac { x - 2 } { 1 } = \frac { y + 2 } { 2 } = \frac { z - 3 } { 3 }
\end{aligned}$$

The shortest distance between $L _ { 1 }$ and $L _ { 2 }$ is\\
(A) 0\\
(B) $\frac { 17 } { \sqrt { 3 } }$\\
(C) $\frac { 41 } { 5 \sqrt { 3 } }$\\
(D) $\frac { 17 } { 5 \sqrt { 3 } }$