Thank you for reporting, we will resolve it shortly
Q.
The ratio of maximum and minimum magnitudes of the resultant of two vectors $\vec{a}$ and $\vec{b}$ is $3: 1$ , Now, $|\vec{a}|=$
Motion in a Plane
Solution:
$|\vec{a}+\vec{b}|=\sqrt{a^{2}+b^{2}+2 a b \cos \theta}$
$|\vec{a}+\vec{b}|_{\max }=a+b,$ when $\theta=0^{\circ}$
$|\vec{a}+\vec{b}|_{\min }=a-b$ when $\theta=180^{\circ}$
Here, $\frac{a+b}{a-b}=\frac{3}{1}$
$\Rightarrow a+b=3 a-3 b$
so, $4 b=2 a$ or $a=2 b$
$ \Rightarrow |\vec{a}|=2|\vec{b}|$