Question

The resultant of two vectors A and 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. 2A

Answer 1

The correct option is B $\sqrt{2}A$

As shown in figure, the angle $\theta$ between vectors A and B is ${90}^{\circ }$.
Also A = B. Therefore, the magnitude of the resultant is given by

$R^2=A^2+B^2+2AB\cos \theta$
$=A^2+A^2+2A^2\cos {90}^{\circ }$
$=2A^2$
Or $R=\sqrt{2}A.$
Hence the correct choice is (b)