Question

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

Answer 1

The correct answer is:$(\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}).$
Let $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}.$.
$∴|\vec{a}|=\sqrt{1^2+2^2+3^2}=\sqrt{1+4+9}=\sqrt{14}$
Hence,the direction cosines of $\vec{a}$ are $(\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}).$