Find a vector in the direction of the $\overrightarrow{a}$ = $\hat{i} - 2 \hat{j}$ that has magnitude 7 units.

The correct answer is $ \dfrac{7}{\sqrt5} \hat{i} - \dfrac{14}{\sqrt5} \hat{j}$

Given vector $\overrightarrow{a}$ = $\hat{i} - 2 \hat{j}$

Unit vector in the direction of $\hat{a}$ = $\dfrac{\overrightarrow{a}}{|\overrightarrow{a}|}$= $\dfrac{\hat{i} - 2 \hat{j}}{\sqrt{(1)^2+(-2)^2}}$ = $\dfrac{\hat{i} - 2 \hat{j}}{\sqrt5}$


∴ Vector in the direction $\overrightarrow{a}$ that has magnitude 7 units = $7 \left( \dfrac{\hat{i} - 2 \hat{j}}{\sqrt5} \right)$ = $ \dfrac{7}{\sqrt5} \hat{i} - \dfrac{14}{\sqrt5} \hat{j}$