Two vectors A→and B→ are such that A→+B→=A→-B→. The angle between the vectors A→ and B→ is :

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 :

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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