Question

The direction cosines of a line are $\frac{1}{2},\frac{1}{2},k$ and $k>0$, then $k=?$

Answer 1

Given directional cosines $l,m,n$ are $\frac{1}{2},\frac{1}{2},k$

$l^2+m^2+n^2=1\frac{1}{4}+\frac{1}{4}+k^2=1\frac{1}{2}+k^2=1k^2=\frac{1}{2}k=\frac{1}{\sqrt{2}}or\frac{-1}{\sqrt{2}}$

Given that $k>0$

$\therefore k=\frac{1}{\sqrt{2}}$