Question

Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. If magnitude of $\overrightarrow{ A }+\overrightarrow{ B }$ is equal to two times the magnitude of $\overrightarrow{ A }-\overrightarrow{ B }$, then the angle between $\overrightarrow{ A }$ and $\overrightarrow{ B }$ will be:

• A. $\sin ^{-1}\left(\frac{3}{5}\right)$
• B. $\sin ^{-1}\left(\frac{1}{3}\right)$
• C. $\cos ^{-1}\left(\frac{3}{5}\right)$
• D. $\cos ^{-1}\left(\frac{1}{3}\right)$

Answer 1

Answer: (C)

$\left(a^{2}+b^{2}+2 a b \cos \theta\right)=4\left(a^{2}+b^{2}-2 a b \cos \theta\right)$
put $a=b$ we get
$2 a^{2}+2 a^{2} \cos \theta=8 a^{2}-8 a^{2} \cos \theta$
$\cos \theta=\frac{3}{5}$