Question

We have a vector $\overrightarrow{OA}$ of magnitude $6$ making an angle ${60}^{\circ }$ with the $x-$axis. The resolution of this vector $\overrightarrow{OA}$ in its components is represented as

• A. $\overrightarrow{OA}=3\hat{i}+3\sqrt{3}\hat{j}$
• B. $\overrightarrow{OA}=3\hat{i}+3\hat{j}$
• C. $\overrightarrow{OA}=3\sqrt{3}\hat{j}$
• D. $\overrightarrow{OA}=3\sqrt{3}\hat{i}+3\sqrt{3}\hat{j}$

Answer 1

The correct option is A $\overrightarrow{OA}=3\hat{i}+3\sqrt{3}\hat{j}$

Since a vector $\overrightarrow{AB}$ having magnitude $r$
making an angle $\theta$ with the $x-$axis can be represented as
$\overrightarrow{AB}=r\cos \theta \hat{i}+r\sin \theta \hat{j}$

Therefore, we can write our given vector as $\overrightarrow{OA}=6\cos {60}^{\circ }\hat{i}+6\sin {60}^{\circ }\hat{j}$

$\overrightarrow{OA}=3\hat{i}+3\sqrt{3}\hat{j}$

Hence, option $\left(\text{A}\right)$ is the right choice.