Question

Find a unit vector parallel to the vector $-3\hat{i}+4\hat{j}$.

Answer 1

Let $\overrightarrow{a}=-3\hat{i}+4\hat{j}$.

Then,

$|\overrightarrow{a}|=\sqrt{2^2+(-1{)}^2}=\sqrt{5}$

Therefore,

A unit vector parallel to $\overrightarrow{a}$ is $\hat{a}=\frac{\overrightarrow{a}}{|\overrightarrow{a}|}$.

$\hat{a}=\frac{1}{\sqrt{5}}(2\hat{i}-\hat{j})=\frac{2}{\sqrt{5}}\hat{i}-\frac{1}{\sqrt{5}}\hat{j}$

Hence, required vector = $5\hat{a}=5(\frac{2}{\sqrt{5}}\hat{i}-\frac{1}{\sqrt{5}}\hat{j})=2\sqrt{5}\hat{i}-\sqrt{5}\hat{j}$.