Question

If |$\overrightarrow{A}$ + $\overrightarrow{B}$| = |$\overrightarrow{A}$-$\overrightarrow{B}$|, then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ will be

• A. 30${}^{\circ }$
• B. 45${}^{\circ }$
• C. 60${}^{\circ }$
• D. 90${}^{\circ }$

Answer 1

The correct option is D 90${}^{\circ }$

Let $\theta$ be the angle between the vectors A and $\overrightarrow{B}$. Then$|\overrightarrow{A}$ + $\overrightarrow{B}|$ = $\sqrt{A^2+B^2+ABcos\theta }$

$|\overrightarrow{A}$ - $\overrightarrow{B}|$ = $\sqrt{A^2+B^2-ABcos\theta }$

According to given problem$|\overrightarrow{A}$ + $\overrightarrow{B}|$=$\overrightarrow{|}A$ - $\overrightarrow{B}|$

$\sqrt{A^2+B^2+ABcos\theta }$ = $\sqrt{A^2+B^2-ABcos\theta }$

Squaring both sides, we get$A^2+B^2+ABcos\theta$ = $A^2+B^2-ABcos\theta$

$\therefore$ 4ABcos$\theta$ =0As A$\ne$0, B$\ne$0$\therefore$ cos$\theta$=0 or $\theta$= 90${}^{\circ }$