Question

Find the angles which the vector $\overrightarrow{a}=3\hat{i}-6\hat{j}+2\hat{k}$ makes with the coordinate axes ?

Answer 1

$\begin{array}{c}\overrightarrow{a}=3\hat{i}-6\hat{j}+2\hat{k}\\ \left|\overrightarrow{a}\right|=\sqrt{3^2+6^2+2^2}=7\end{array}$

The angles made with the coordinate axes are

$\alpha ={\cos }^{-1}\frac{3}{7};\beta ={\cos }^{-1}\frac{-6}{7};\gamma ={\cos }^{-1}\frac{2}{7}$