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If the magnitude of addition of two vectors is equal to the magnitude of subtraction of these two vectors

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These two vectors are parallel

These two vectors are anti parallel

These two vectors are perpendicular

These two vectors are inclined at $120^{\circ}$

answer is C.

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Detailed Solution

$| \bar{A} + \bar{B} | = | \bar{A} - \bar{B} |$

$\sqrt{A^{2} + B^{2} + 2 ABcos θ} = \sqrt{A^{2} + B^{2} - 2 ABcos θ}$

$\Rightarrow A^{2} + B^{2} + 2 ABcos θ = A^{2} + B^{2} - 2 ABcos θ$

$\Rightarrow 4 ABcos θ = 0$

$\cos θ = 0$

$θ = 90^{\circ}$

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