Question

The perpendicular distance of the point (2, 4, –1) from the line $\frac { x + 5 } { 1 } = \frac { y + 3 } { 4 } = \frac { z - 6 } { - 9 }$ is

• A. 3
• B. 5
• C. 7
• D. 9

Answer 1

Answer: (C)

7

Answer 2

The perpendicular distance of (2, 4, – 1) from the line $\frac { x + 5 } { 1 } = \frac { y + 3 } { 4 } = \frac { z - 6 } { - 9 }$ is $\left\{ ( 2 + 5 ) ^ { 2 } + ( 4 + 3 ) ^ { 2 } + ( - 1 - 6 ) \right.$

$\left. - \left[ \frac { 1 ( 2 + 5 ) + 4 ( 4 + 3 ) - 9 ( - 1 - 6 ) } { \sqrt { 1 + 16 + 81 } } \right] ^ { 2 } \right\} ^ { 1 / 2 }$

$= \sqrt { 147 - \left( \frac { 98 } { \sqrt { 98 } } \right) ^ { 2 } }$ $= \sqrt { 147 - 98 } = \sqrt { 49 } = 7$.