Question

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

Moderate

Solution

$| \vec{A} + \vec{B} | = | \vec{A} - \vec{B} | = θ = 90^{0}$
${(A)}^{2} + {(B)}^{2} + 2 (A) (B) cosθ = {(A)}^{2} + {(B)}^{2} - 2 (A) (B) cosθ$
$2 cosθ = 0 \Rightarrow θ = 90^{0}$

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