Question

Find the vector parallel to the vector $\hat{i}-2\hat{j}$ and has magnitude $2\sqrt{5}$ units.

• A. $2\hat{i}+4\hat{j}$
• B. $2\hat{i}-4\hat{j}$
• C. $3\hat{i}-4\hat{j}$
• D. $2\hat{i}-3\hat{j}$

Answer 1

The correct option is B $2\hat{i}-4\hat{j}$

Let $\overrightarrow{a}=\hat{i}-2\hat{j}$
So, $|\overrightarrow{a}|=\sqrt{1^2+(-2{)}^2}=\sqrt{5}$
Thus, the unit vector is given as
$\hat{a}=\frac{\overrightarrow{a}}{|\overrightarrow{a}|}$
$\Rightarrow \hat{a}=\frac{\hat{i}-2\hat{j}}{\sqrt{5}}$

Let $\overrightarrow{b}$ be the vector parallel to $\overrightarrow{a}$ having magnitude $2\sqrt{5}$ units
$\therefore$ $|\overrightarrow{b}|=2\sqrt{5}$
Now, $\overrightarrow{b}=|\overrightarrow{b}|.\hat{a}\Rightarrow \left(2\sqrt{5}\right).\frac{\hat{i}-2\hat{j}}{\sqrt{5}}$
$\Rightarrow \overrightarrow{b}=2\hat{i}-4\hat{j}$