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If O is the origin and $P (x_{1}, y_{1}), Q (x_{2}, y_{2})$ are two points $O P \times O Q \sin ∠ P O Q =$

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x1x2+y1y2

x1y2+x2y1

x1y2−x2y1

none of these

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detailed solution

Correct option is C

We, have,Area of ΔOPQ=Absolute value of 120 0 1x1 y1 1x2 y2 1⇒ Area of ΔOPQ=12x1y2−x2y1Also, Area of ΔOPQ=12OP×OQ×sin⁡∠POQ∴ 12OP×OQsin⁡∠POQ=12x1y2−x2y1⇒ OP×OQsin⁡∠POQ=x1y2−x2y1

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If O is the origin and Px1,y1,Qx2,y2 are two points OP×OQsin⁡∠POQ=

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If O is the origin and $P (x_{1}, y_{1}), Q (x_{2}, y_{2})$ are two points $O P \times O Q \sin ∠ P O Q =$