1.

If the coordinates of any two points Q_1 and Q_2 are (x_1,y_1) and (x_2,y_2), respectively, then prove that OQ_1xxOQ_2cos(angleQ_1OQ_2)=x_1x-2+y-1y_2, whose O is the origin.

Answer»

Solution :
In `DeltaOQ_1Q_2`, using cosing rule, we get
`(Q-1Q_2)^2=(OQ_1)^2+(OQ_2)^2-OQ_1.OQ_2.cos(angleQ_1OQ_2)`
`therefore(x_2-x_1)^2+(y_2-y_1)^2`
`=(x_(1)^2+y_1^2)+(x_2^2+y_2^2)-2OQ_1.OQ_2.cos(angleQ_1OQ_2)`
`rArrOQ_1.OQ_2cos(angleQ_1OQ_2)=x_1x_2+y_1y_2`.


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