Question

Vector $A$ and $B$ are as shown in the figure having magnitude of $2$ units each. Find $\overrightarrow{A}+\overrightarrow{B}$.

• A. $0$
• B. $2\hat{i}$
• C. $2\hat{j}$
• D. $2\hat{i}+2\hat{j}$

Answer 1

The correct option is C $2\hat{j}$

Since, $A$ and $B$ have same magnitudes, there horizontal component will cancel each other and verticle components will be added.
Thus, we have
$\overrightarrow{A}+\overrightarrow{B}$
= (2 sin(30 ${}^{\circ }$) + 2 sin(30 ${}^{\circ }$)) $\hat{j}$
= 2 $\hat{j}$