Question

Two $\overrightarrow{a}$ and $\overrightarrow{b}$ are at an angle of ${60}^o$ with each other Their resultant makes an angle of ${45}^o$ with $\overrightarrow{a}$ If magnitude $|\overrightarrow{b}|=2$ units then $|\overrightarrow{a}|$ is:

• A. $\sqrt{3}$
• B. $\sqrt{3}-1$
• C. $\sqrt{3}+1$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is B $\sqrt{3}-1$

The vectors make $60°$ with each other, and the resultant vector makes $45°$ with $a$

The other angle $=15°$

Using the side rule;

$a/\sin 15=2/\sin 45a=2\sin 15/\sin 45a=0.732$

Hence correct answer is $\left(B\right)$ $\sqrt{3}-1$