Question

The ratio of maximum and minimum magnitudes of the resultant of two vectors $\vec{a}$ and $\vec{b}$ is $3:1$ , Now, $|\vec{a}|=$

• A. $|\vec{b}|$
• B. $2|\vec{b}|$
• C. $3|\vec{b}|$
• D. $4|\vec{b}|$

Answer 1

Answer: (B)

$|\vec{a}+\vec{b}|=\sqrt{a^2+b^2+2ab\cos \theta }$
$|\vec{a}+\vec{b}{|}_{\max }=a+b,$ when $\theta =0^{\circ }$
$|\vec{a}+\vec{b}{|}_{\min }=a-b$ when $\theta =180^{\circ }$
Here, $\frac{a+b}{a-b}=\frac{3}{1}$
$\Rightarrow a+b=3a-3b$
so, $4b=2a$ or $a=2b$
$\Rightarrow |\vec{a}|=2|\vec{b}|$