Question

The vector $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $|A+B|=|A-B|$ . The angle between vector $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

• A. ${90}^o$
• B. ${60}^o$
• C. ${75}^o$
• D. ${45}^o$

Answer 1

The correct option is A ${90}^o$

Given that,

Two vectors are $\overrightarrow{A}$ and $\overrightarrow{B}$

Now, the addition

$|A+B{|}^2=|A{|}^2+|B{|}^2+2|A||B|cos\theta$

Now, the subtraction

$|A-B{|}^2=|A{|}^2+|B{|}^2-2|A||B|cos(180-\theta )$

By the given condition

$|A+B|=|A-B|$

So,

$|A{|}^2+|B{|}^2+2|A||B|cos\theta =|A{|}^2+|B{|}^2-2|A||B|cos(180-\theta )$

$\cos \theta =\cos ({180}^0-\theta )$

$2\theta ={180}^0$

$\theta ={90}^0$

Hence, the angle is ${90}^0$