Statement I : $If | \vec{A} + \vec{B} | = | \vec{A} - \vec{B} |, then angle between \vec{A} and \vec{B} is 90^{0}$
Statement II : $\vec{A} + \vec{B} = \vec{B} + \vec{A}$

Moderate

A

If both statement I and statement II are true and statement II is the correct explanation of statement I.
B

If both statement I and statement II are true but statement II is not the correct explanation of statement I.
C

If statement I is true but statement II is false.
D

If both statement I and statement II are false.

Solution

$| \vec{A} + \vec{B} | = | \vec{A} - \vec{B} |$
$\Rightarrow A^{2} + B^{2} + 2 ABcosθ = A^{2} + B^{2} - 2 ABcosθ$
Hence $cosθ = 0 which gives θ = 90^{0}$
Also vector addition is commutative.
Hence $\vec{A} + \vec{B} = \vec{B} + \vec{A}$

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