The direction cosines of three mutually perpendicular straight lines are $〈l_{1}, m_{1}, n_{1}〉, 〈l_{2}, m_{2}, n_{2}〉, 〈l_{3}, m_{3}, n_{3}〉$ . Then the direction cosines of a line which is equally inclined to the given three lines, are

Moderate

A

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

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

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

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

Solution

Given $〈l_{1}, m_{1}, n_{1}〉, 〈l_{2}, m_{2}, n_{2}〉, 〈l_{3}, m_{3}, n_{3}〉$ are the direction cosines of three mutually perpendicular lines
It implies that $\sum l_{1} l_{2} = \sum l_{2} l_{3} = \sum l_{1} l_{3} = 0, \sum {l_{1}}^{2} = \sum {l_{2}}^{2} = \sum {l_{3}}^{2} = 1$
Hence the direction cosines of line which is equally inclined to the above lines are $(\frac{l_{1} + l_{2} + l_{3}}{3}, \frac{m_{1} + m_{2} + m_{3}}{3}, \frac{n_{1} + n_{2} + n_{3}}{3},)$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

SCAN ME