MCQ
The vectors $\vec{A}$ and $\vec{B}$ are such that
$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$
The angle between the two vectors is
- A$60$
- B$75$
- C$45$
- ✓$90$
✓
Answer
Correct option: D.
$90$
d
The formula for $|\vec{A}+\vec{B}|^{2}$ is,
The formula for $|\vec{A}+\vec{B}|^{2}$ is,
$|\vec{A}+\vec{B}|^{2}=|\vec{A}|^{2}+|\vec{B}|^{2}+2 \vec{A} \cdot \vec{B}$
$=A+B+2 A B \cos \theta$ And The formula for $|\vec{A}-\vec{B}|^{2}$ is,
$|\vec{A}-\vec{B}|^{2}=|\vec{A}|^{2}+|\vec{B}|^{2}-2 \vec{A} \cdot \vec{B}$
$=A+B-2 A B \cos \theta$
It is given that,
$|\vec{A}+\vec{B}|^{2}=|\vec{A}-\vec{B}|^{2}$
$A+B+2 A B \cos \theta=A+B-2 A B \cos \theta$
$4 A B \cos \theta=0$
$\cos \theta=0$
$\theta=90^{\circ}$
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