Question

The shortest distance between the lines $\frac { x - 1 } { 2 } = \frac { y - 2 } { 3 } = \frac { z - 3 } { 4 }$ and $\frac { x - 2 } { 3 } = \frac { y - 4 } { 4 } = \frac { z - 5 } { 5 }$ is

• A. $\frac { 1 } { 6 }$
• B. $\frac { 1 } { \sqrt { 6 } }$
• C. $\frac { 1 } { \sqrt { 3 } }$
• D. $\frac { 1 } { 3 }$

Answer 1

Answer: (B)

$\frac { 1 } { \sqrt { 6 } }$

Answer 2

S.D.$= \frac { \left| \begin{array} { c c c } 2 - 1 & 4 - 2 & 5 - 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{array} \right| } { \sqrt { ( 15 - 16 ) ^ { 2 } + ( 12 - 10 ) ^ { 2 } + ( 8 - 9 ) ^ { 2 } } } = \frac { \left| \begin{array} { l l l } 1 & 2 & 2 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{array} \right| } { \sqrt { 1 + 1 + 4 } } = \frac { 1 } { \sqrt { 6 } }$.