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Q.

The sum and difference of two perpendicular vectors of equal length are

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a

Perpendicular to each other and of different lengths

b

Of equal length and have an obtuse angle between them

c

Perpendicular to each other and of equal length

d

Of equal length and have an acute angle between them

answer is A.

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Detailed Solution

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Given $| \vec{A} | = | \vec{B} | or A = B$
Sum $\vec{R} = \vec{A} + \vec{B}$
$\Rightarrow | \vec{R} | = \sqrt{A^{2} + B^{2}} = \sqrt{2 A}$
Difference $\vec{S} = \vec{A} - \vec{B}$
$\Rightarrow | \vec{S} | = \sqrt{A^{2} - B^{2}} = \sqrt{2} A$
$α_{1} = 45^{0}, α_{2} = 45^{0}$
Hence, $\vec{R}$ and $\vec{S}$ will be perpendicular and also of equal lengths

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