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Q.

If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude R are inclined at angle θ, then

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a

$|\vec{A} + \vec{B}| = 2 R \cos (\frac{θ}{2})$

b

$|\vec{A} - \vec{B}| = 2 R \cos (\frac{θ}{2})$

c

$|\vec{A} - \vec{B}| = \sqrt{2} R \sin (\frac{θ}{2})$

d

$|\vec{A} + \vec{B}| = 2 R \sin (\frac{θ}{2})$

answer is A.

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Detailed Solution

$\begin{array}{l} |\vec{A} + \vec{B}| = 2 R \cos \frac{θ}{2} \\ |\vec{A} - \vec{B}| = 2 R \sin \frac{θ}{2} \end{array}$

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If two vectors A→ and B→ having equal magnitude R are inclined at angle θ, then