First slide

Vectors

Question

Two vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$ . The angle between the vectors $\vec{A}$ and $\vec{B}$ is :

Moderate

A

0
B

$π$ /3
C

$π$ /2
D

$π$

Solution

$|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}| \Rightarrow \sqrt{A^{2} + B^{2} +2 ABcosθ}$ $= \sqrt{A^{2} + B^{2} - 2 ABcosθ} \Rightarrow \cos θ = 0 \Rightarrow θ = \frac{π}{2}$ .

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