Practicing Success
The angle between lines whose direction cosines are given by $\ell+m+n=0$, $\ell^2+m^2-n^2=0$, is : |
$\frac{\pi}{2}$ $\frac{\pi}{3}$ $\frac{\pi}{6}$ None of these |
None of these |
$\ell+m+n=0, \ell^2+m^2-n^2=0$ We also have $\ell^2+m^2+n^2=1 $ $\Rightarrow 2 n^2=1 $ $\Rightarrow n=\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$ Also, $\ell^2+m^2=n^2=(-(\ell+m))^2$ $\Rightarrow \ell m=0$ and $\ell+m= \pm \frac{1}{\sqrt{2}}$ Hence, direction cosines are lines are $\left(\frac{1}{\sqrt{2}}, 0,-\frac{1}{\sqrt{2}}\right),\left(-\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}\right), $ $\left(0, \frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right),\left(0,-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ Angle between these lines in both cases is zero. |