Question

If $\overrightarrow{b}=3\hat{i}+4\hat{j}$ and $\overrightarrow{a}=\hat{i}-\hat{j}$, the vector having the same magnitude as that of $\overrightarrow{b}$ and parallel to $\overrightarrow{a}$ is ______.

• A. $\frac{5}{\sqrt{2}}(\hat{i}-\hat{j})$
• B. $\frac{5}{\sqrt{2}}(\hat{i}+\hat{j})$
• C. $5(\hat{i}-\hat{j})$
• D. $5(\hat{i}+\hat{j})$

Answer 1

The correct option is A $\frac{5}{\sqrt{2}}(\hat{i}-\hat{j})$

$\left|\overrightarrow{b}\right|=\sqrt{3^2+4^2}=5$

unit vector $\parallel$ to $\hat{a}=\frac{1}{\sqrt{2}}\hat{i}-\frac{1}{\sqrt{2}}\hat{j}$

$\therefore$ Required Vector $=\left|b\right|.\hat{a}=\frac{5}{\sqrt{2}}\hat{i}-\frac{5}{\sqrt{2}}\hat{j}$.