Question

Vector $\overrightarrow{A}$ is of length 2 cm and is ${60}^{\circ }$ above the x -axis in the first quadrant. Vector $\overrightarrow{B}$ is of length 2 cm and ${60}^{\circ }$ below the x-axis in the fourth quadrant. The sum $\overrightarrow{A}+\overrightarrow{B}$ is a vector of magnitude (cm).

• A. 2 along +y-axis
• B. 2 along +x-axis
• C. 1 along -x-axis
• D. 2 along -x-axis

Answer 1

The correct option is B 2 along +x-axis

Let us assume,
$\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}$
$=(A\cos 60\hat{i}+A\sin 60\hat{j})+(B\cos 60\hat{i}-B\sin 60\hat{j})$
$\because |\overrightarrow{A}|=|\overrightarrow{B}|=2cm$
So, $R=(A\cos 60+B\cos 60)\hat{i}=2\hat{i}$
Hence $2cm$ along + x -axis