Question

Find the direction angles and direction cosines of the following vectors:
$(1,0,-1)$

Answer 1

let the given vector be $\overrightarrow{x}=(1,0,-1)$

$\Rightarrow |\overrightarrow{x}|=\sqrt{1^2+0^2+(-1{)}^2}=\sqrt{2}$

Therefore, direction cosines are $(\frac{1}{\sqrt{2}},0,\frac{-1}{\sqrt{2}})$

Direction angles are given by

$\Rightarrow \left({\cos }^{-1}\right(\frac{1}{\sqrt{2}}),{\cos }^{-1}(0),{\cos }^{-1}(\frac{-1}{\sqrt{2}}\left)\right)$

$\Rightarrow (\frac{\pi }{4},\frac{\pi }{2},\frac{\pi }{4})$