Question

Find the direction angles and direction cosines of the following vectors:
$\hat{j}+\hat{k}$

Answer 1

Let $\overrightarrow{a}=\hat{j}+\hat{k}=(0,1,1)$

$\Rightarrow |\overrightarrow{a}|=\sqrt{1^2+1^2}=\sqrt{2}$

$\Rightarrow$Direction ratios $=(0,\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$

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

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