The direction cosines of a line equally inclined to three mutually perpendicular lines having direction cosines as $l_{1}, m_{1}, n_{1}; l_{2}, m_{2}, n_{2} a n d l_{3}, m_{3}, n_{3}$ are

Moderate

A

$l_{1} + l_{2} + l_{3}, m_{1} + m_{2} + m_{3}, n_{1} + n_{2} + n_{3}$
B

$\frac{l_{1} + l_{2} + l_{3}}{\sqrt{3}}, \frac{m_{1} + m_{2} + m_{3}}{\sqrt{3}}, \frac{n_{1} + n_{2} + n_{3}}{\sqrt{3}}$
C

$\frac{l_{1} + l_{2} + l_{3}}{3}, \frac{m_{1} + m_{2} + m_{3}}{3}, \frac{n_{1} + n_{2} + n_{3}}{3}$
D

$\frac{l_{1} + l_{2} + l_{3}}{9}, \frac{m_{1} + m_{2} + m_{3}}{9}, \frac{n_{1} + n_{2} + n_{3}}{9}$

Solution

Since the three lines are mutually perpendicular,
$l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2} = 0$
$l_{2} l_{3} + m_{2} m_{3} + n_{2} n_{3} = 0$
$l_{3} l_{1} + m_{3} m_{1} + n_{3} n_{1} = 0$

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