Question

The length of the perpendicular drawn from the point

(5, 4, –1) on the line $\frac { x - 1 } { 2 } = \frac { y } { 9 } = \frac { z } { 5 }$ is

• A. $\sqrt { \frac { 110 } { 2109 } }$
• B. $\sqrt { \frac { 2109 } { 110 } }$
• C. $\frac { 2109 } { 110 }$
• D. 54

Answer 1

Answer: (B)

$\sqrt { \frac { 2109 } { 110 } }$

Answer 2

Required distance

$= \sqrt { ( 5 - 1 ) ^ { 2 } + ( 4 - 0 ) ^ { 2 } + ( - 1 - 0 ) ^ { 2 } - \left[ \frac { ( 5 - 1 ) 2 + ( 4 - 0 ) 9 + ( - 1 - 0 ) 5 } { \sqrt { 4 + 81 + 25 } } \right] ^ { 2 } }$

$\sqrt { 33 - \frac { 39 \times 39 } { 110 } } = \sqrt { \frac { 2109 } { 110 } }$.