Question

Find a vector in the direction of the vector $\overrightarrow{a}=(3\hat{i}+\hat{j})$ that has magnitude 5 units.

Answer 1

$\begin{array}{c}\overrightarrow{a}=3\hat{i}+\hat{j}\\ Unitvectorinthedirectionof\overrightarrow{a}=\frac{3\hat{i}+\hat{j}}{\sqrt{10}}\\ \overrightarrow{b}=5\hat{a}\\ =\frac{5\left(3\hat{i}+\hat{j}\right)}{\sqrt{10}}\\ =\frac{\sqrt{5}}{\sqrt{2}}\left(3\hat{i}+\hat{j}\right)\end{array}$

Hence, this is the answer.