If the direction cosines of two lines are such that $l+m+n=0, l^2+m^2-n^2=0$, then the angle between them is :
If the direction cosines of two lines are such that $l+m+n=0, l^2+m^2-n^2=0$, then the angle between them is :
$\pi$
$\pi / 3$
$\pi / 4$
$\pi / 6$
Solution
If $l, m, n$ are direction cosines of two lines are such that
$l+m+n=0$ $\ldots$ (i)
$l^2+m^2-n^2=0$ ...(ii)
and $l^2+m^2+n^2=1$ ...(iii)
On solving Eqs. (i), (ii) and (iii), we get $l=0, m= \pm \frac{1}{\sqrt{2}}$ and $n= \pm \frac{1}{\sqrt{2}}$
$\therefore$ Angle between these two lines
$=\frac{\pi}{3} \text { or } \frac{\pi}{2}$