The angle between the lines whose direction cosines satisfy the e… - Vidyadip

MCQ

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$, ${l^2} + {m^2} - {n^2} = 0$ is given by

A
$\frac{{2\pi }}{3}$
B
$\frac{\pi }{6}$
C
$\frac{{5\pi }}{6}$
✓
$\frac{\pi }{3}$

✓

Answer

Correct option: D.

$\frac{\pi }{3}$

d
(d) $l + m + n = 0,\,\,{l^2} + {m^2} - {n^2} = 0$ and ${l^2} + {m^2} + {n^2} = 1$

Solving above equations, we get $m = \pm \frac{1}{{\sqrt 2 }},\,\,n = \pm \frac{1}{{\sqrt 2 }}$ and $l = 0$.

$\therefore \,\,\,\theta = \frac{\pi }{3}$ or $\frac{\pi }{2}$.

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