Question

For which angle between two equal vectors $\vec{A}$ and $\vec{B}$ will the magnitude of the sum of two vectors be equal to the magnitude of each vector?

• A. $\theta=60^{\circ}$
• B. $\theta=120^{\circ}$
• C. $\theta=0^{\circ}$
• D. $\theta=90^{\circ}$

Answer 1

Answer: (C)

$|\vec{A}+\vec{B}|=\sqrt{A^{2}+B^{2}+2 A B \cos 120^{\circ}}$
$\left(\theta=120^{\circ}\right)$
$=\sqrt{A^{2}+B^{2}+\text{not} 2 A B\left(\frac{-1}{\text{not} 2}\right)}\left(\cos 120^{\circ}=-\frac{1}{2}\right)$
$=\sqrt{A^{2}+B^{2}-A(A)}=\sqrt{B^{2}}=B$
$(\therefore A=B)$