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If O is the origin and $P (x_{1}, y_{1}), Q (x_{2}, y_{2})$ are two points, then $O P . O Q \cos ∠ P O Q$

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x1x2+y/1y2

x1y2+x2y1

x1 y2 −x2 y1

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Correct option is A

Using cosine formula in ∆POQ we havePQ2=OP2+OQ2−2OP×OQcos⁡∠POQ⇒ x1−x22+y1−y22=x12+y12+x22+y22−2OP×OQcos⁡∠POQ⇒OP⋅OQcos⁡∠POQ=x1x2+y1y2

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If O is the origin and Px1,y1,Qx2,y2 are two points, then OP.OQ cos⁡∠POQ

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If O is the origin and $P (x_{1}, y_{1}), Q (x_{2}, y_{2})$ are two points, then $O P . O Q \cos ∠ P O Q$