Question

Find a unit vector parallel to the vector $\hat{i}+\sqrt{3}\hat{j}$.

Answer 1

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