Question

Find the direction angles and direction cosines of the following vectors:
$5\hat{i}+12\hat{j}+84\hat{k}$

Answer 1

Let $\overrightarrow{a}=\hat{j}+\hat{k}=(5,12,84)$

$\Rightarrow |\overrightarrow{a}|=\sqrt{(5{)}^2+(12{)}^2+(84{)}^2}=85$

$\Rightarrow$Direction ratios $=(\frac{5}{85},\frac{12}{85},\frac{84}{85})$

$\Rightarrow$Direction ratios $=(\frac{1}{17},\frac{12}{85},\frac{84}{85})$

$\Rightarrow$Direction angles $=\left({\cos }^{-1}\right(\frac{1}{17}),{\cos }^{-1}(\frac{12}{85}),{\cos }^{-1}(\frac{84}{85}\left)\right)$