Question

Find a vector of magnitude 4 units which is parallel to the vector $\sqrt{3}\hat{i}+\hat{j}$.

Answer 1

Let $\overrightarrow{a}=\sqrt{3}\hat{i}+\hat{j}$
Then, $\left|\overrightarrow{a}\right|=\sqrt{{\left(\sqrt{3}\right)}^2+1}=\sqrt{3+1}=\sqrt{4}=2$
A unit vector parallel to $\overrightarrow{a}$ = $\hat{a}=\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}=\frac{1}{2}\left(\sqrt{3}\hat{i}+\hat{j}\right)$
Hence, Required vector = $4\hat{a}=4\times \frac{1}{2}\left(\sqrt{3}\hat{i}+\hat{j}\right)=2\sqrt{3}\hat{i}+2\hat{j}$