Question

If $|\overrightarrow{A}|=|\overrightarrow{B}|$, then what is the angle between $\overrightarrow{A}+\overrightarrow{B}$ and $\overrightarrow{A}-\overrightarrow{B}$:

• A. ${90}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. $0^{\circ }$

Answer 1

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

$(\overrightarrow{A}+\overrightarrow{B})\cdot (\overrightarrow{A}-\overrightarrow{B})=A^2-\overrightarrow{A}\cdot \overrightarrow{B}+\overrightarrow{B}\cdot \overrightarrow{A}-B^2=A^2-B^2=0$
Dot product of two vector is zero only when angle between them is ${90}^o$