Question

The shortest distance between the lines $\frac { x - 3 } { 3 } = \frac { y - 8 } { - 1 } = \frac { z - 3 } { 1 }$ and $\frac { x + 3 } { - 3 } = \frac { y + 7 } { 2 } = \frac { z - 6 } { 4 }$ is

• A. $\sqrt { 30 }$
• B. $2 \sqrt { 30 }$
• C. $5 \sqrt { 30 }$
• D. $3 \sqrt { 30 }$

Answer 1

Answer: (D)

$3 \sqrt { 30 }$

Answer 2

S.D.$=$ $\frac { \left| \begin{array} { c c c } 6 & 15 & - 3 \\ 3 & - 1 & 1 \\ - 3 & 2 & 4 \end{array} \right| } { \sqrt { ( - 4 - 2 ) ^ { 2 } + ( 12 + 3 ) ^ { 2 } + ( 6 - 3 ) ^ { 2 } } }$

$= \frac { 270 } { \sqrt { 270 } } = \sqrt { 270 }$ = $3 \sqrt { 30 }$.