If R¯=P¯+Q¯ where R¯,P¯,Q¯ are non-zero vectors. If |R¯|=|P¯|=|Q¯| then angle between R¯ and P¯

R=2Pcos⁡θ2⇒P=2Pcos⁡θ2Cos⁡θ2=12⇒θ2=60∘θ=120∘∴ Angle b /w P¯ and R¯=60∘

If R¯=P¯+Q¯ where R¯,P¯,Q¯ are non-zero vectors. If |R¯|=|P¯|=|Q¯| then angle between R¯ and P¯

R=2Pcos⁡θ2⇒P=2Pcos⁡θ2Cos⁡θ2=12⇒θ2=60∘θ=120∘∴ Angle b /w P¯ and R¯=60∘

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If $\bar{R} = \bar{P} + \bar{Q} where \bar{R}, \bar{P}, \bar{Q}$ are non-zero vectors. If $| \bar{R} | = | \bar{P} | = | \bar{Q} |$ then angle between $\bar{R} and \bar{P}$

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$\frac{π}{3}$

$\frac{2 π}{3}$

$\frac{π}{4}$

$\frac{π}{6}$

answer is A.

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Detailed Solution

$\begin{array}{rcl} R & = & 2 Pcos \frac{θ}{2} \Rightarrow P = 2 Pcos \frac{θ}{2} \\ Cos \frac{θ}{2} & = & \frac{1}{2} \Rightarrow \frac{θ}{2} = 60^{\circ} \\ θ & = & 120^{\circ} \\ ∴ Angle b / w \bar{P} and \bar{R} & = & 60^{\circ} \end{array}$