Question

Find the direction cosines of the vector $\hat{i}+2\hat{j}+3\hat{k}$

Answer 1

Let $a=\hat{i}+2\hat{j}+3\hat{k}$
Then, $|a|=\sqrt{1^2+2^2+3^2}=\sqrt{14}$
$\therefore \hat{a}=\frac{a}{|a|}\Rightarrow \hat{a}=\frac{1}{\sqrt{14}}(\hat{i}+2\hat{j}+3\hat{k})$
$\Rightarrow \hat{a}=\frac{1}{\sqrt{14}}\hat{i}+\frac{2}{\sqrt{14}}\hat{j}+\frac{3}{\sqrt{40}}\hat{k}$
Hence, direction cosines of the given vector are $\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}$