Question

The direction cosines of the normal to the plane $3 x + 4 y + 12 z = 52$ will be

• A. 3, 4, 12
• B. – 3, – 4, – 12
• C. $\frac { 3 } { 13 } , \frac { 4 } { 13 } , \frac { 12 } { 13 }$
• D. $\frac { 3 } { \sqrt { 13 } } , \frac { 4 } { \sqrt { 13 } } , \frac { 12 } { \sqrt { 13 } }$

Answer 1

Answer: (C)

$\frac { 3 } { 13 } , \frac { 4 } { 13 } , \frac { 12 } { 13 }$

Answer 2

Direction ratio of normal to the plane

$3 x + 4 y + 12 z = 52$ is 3, 4, 12.

$\therefore$D.c's are $\left( \frac { 3 } { \sqrt { 3 ^ { 2 } + 4 ^ { 2 } + 12 ^ { 2 } } } , \frac { 4 } { \sqrt { 3 ^ { 2 } + 4 ^ { 2 } + 12 ^ { 2 } } } , \frac { 12 } { \sqrt { 3 ^ { 2 } + 4 ^ { 2 } + 12 ^ { 2 } } } \right)$

$= \left( \frac { 3 } { 13 } , \frac { 4 } { 13 } , \frac { 12 } { 13 } \right)$ .