Question

The resultant of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ subtends an angle of ${45}^{\circ }$ with either of them. The magnitude of the resultant is

• A. zero
• B. $\sqrt{2}$ A
• C. A
• D. 2 A

Answer 1

The correct option is B

$\sqrt{2}$ A

As shown in the figure, the angle $\theta$ between vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${90}^{\circ }$. Also A = B.
Therefore, the magnitude of the resultant is given by
$R^2=A^2+B^2+2ABcos\theta$
$=A^2+A^2+2A^{2}cos{90}^{\circ }$
$=2A^2$
$\therefore R=\sqrt{2}A$.

Hence, the correct choice is (b).