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Q.

If $|\vec{P} + \vec{Q}| = |\vec{P} - \vec{Q}|$ , then the vectors $\vec{P}$ and $\vec{Q}$ are

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a

Perpendicular to each other

b

Parallel to each other

c

Inclined at $60 °$ to each other

d

Inclined at $45 °$ to each other

answer is C.

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Detailed Solution

$|\vec{P} + \vec{Q}| = |\vec{P} - \vec{Q}|$

${|\vec{P} + \vec{Q}|}^{2} = {|\vec{P} - \vec{Q}|}^{2}$

$P^{2} + Q^{2} + 2 PQ \cos θ = P^{2} + Q^{2} - 2 PQ \cos θ$ $4 PQ \cos θ = 0 \Rightarrow \cos θ = 0$

$θ = 90 °$

$\vec{P} ⊥^{r} to \vec{Q}$

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