Question

If $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$ then
a) The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${90}^0$
b) $\overrightarrow{B}=0$

c) $\overrightarrow{A}=0$
d) The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${120}^0$

• A. a, b & c are correct
• B. b, c & d are correct
• C. c, d & a are correct
• D. d, a & b are true

Answer 1

Answer: (A)

a, b & c are correct

The magnitudes of $\overline{A}$ and $\overline{B}$ are equal . Hence, $A^2+B^2+2AB\cos \left(\theta \right)=A^2+B^2-2AB\cos \left(\theta \right)$
$=>2\times 2AB\cos \left(\theta \right)=0$
$=>\cos \left(\theta \right)=0$
$\theta ={90}^0$ or $A=0$ or $B=0$