Question

$A$ and $B$ are the two vectors and the angle between them is ${60}^{\circ }$. If the resultant of these vectors are inclined at an angle of ${45}^{\circ }$ to the vector $B$, then the value of $\frac{B}{A}$ is

• A. $0.453$
• B. $0.732$
• C. $0.366$
• D. $0.588$

Answer 1

The correct option is C $0.366$

Since, the resutant is at ${45}^{\circ }$ to the vector $B$ we have
$\tan {45}^{\circ }=\frac{A\sin {60}^{\circ }}{B+A\cos {60}^{\circ }}=1$
$\Rightarrow A\sin {60}^{\circ }-A\cos {60}^{\circ }=B$
$\Rightarrow \frac{B}{A}=(\sin {60}^{\circ }-\cos {60}^{\circ })=\frac{\sqrt{3}-1}{2}$
$\Rightarrow \frac{B}{A}=0.366$