Question

If $\vec{A}$ and $\vec{B}$ are non-zero vectors which obey the relation $\left|\vec{A}+\vec{B}\right|=\left|\vec{A}-\vec{B}\right|$, then the angle between them is

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

Answer 1

The Correct Option is C

$\left|\vec{A}+\vec{B}\right|=\left|\vec{A}-\vec{B}\right|$ $\left|\vec{A}\right|^{2}+\left|\vec{B}\right|^{2}+2\left|\vec{A}\right|\left|\vec{B}\right|cos \theta$ $=\left|\vec{A}\right|^{2}+\left|\vec{B}\right|^{2}-2\left|\vec{A}\right|\left|\vec{B}\right| cos \theta$ $\therefore\quad cos\theta=0 \Rightarrow \theta= 90^{\circ}$