Question

If resultant of two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ shown in the figure is $\sqrt{7}b$. The value of $\frac{b}{a}$ is

Answer 1

Resultant $R^2=A^2+B^2+2AB\cos \theta$

Or $(\sqrt{7}b{)}^2=a^2+b^2+2ab\cos {60}^o$

Or $7b^2=a^2+b^2+ab$

Or $a^2+ab-6b^2=0$

Or $(a+3b)(a-2b)=0$

$⟹a=2b$

$⟹\frac{b}{a}=2$