If `O` be the origin, and if the coordinates of any two points `P_1`, and `P_2`, be respectively `(x_1, y_1)` and `(x_2,y_2),` prove that: `OP_1. OP_2 .cos P_1OP_2 = x_1.x_2 + y_1.y_2.`

If O is the origin and if the coordinates of any two points Q_1 \ a n d \ Q_2 are (x_1,y_1) \ a n d \ (x_2,y_2), respectively, prove that O Q_1.O Q_2cos/_Q_1O Q_2=x_1x_2+y_1y_2 .

If O is the origin and if the coordinates of any two points Q_1 \ a n d \ Q_2 are (x_1,y_1) \ a n d \ (x_2,y_2), respectively, prove that O Q_1.O Q_2cos/_Q_1O Q_2=x_1x_2+y_1y_2 .

If O is the origin and if the coordinates of any two points Q_(1) and Q_(2) are (x_(1),y_(1)) and (x_(2),y_(2)), respectively,prove that OQ_(1).OQ_(2)cos/_Q_(1)OQ_(2)=x_(1)x_(2)+y_(1)y_(2)

If O is the origin and if the coordinates of any two points Q_1a n dQ_2 are (x_1,y_1)a n d(x_2,y_2), respectively, prove that O Q_1dotO Q_2cos/_Q_1O Q_2=x_1x_2+y_1y_2dot

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.

If O be the origin and if coordinates of any two points Q_(1) and Q_(2) be (x_(1),y_(1)) and (x_(2),y_(2)) respectively, prove that overline(OQ_(1))* overline(OQ_(2)) cos angle Q_(1)OQ_(2)=x_(1)x_(2)+y_(1)+y_(2) .

The co-ordinates of the mid points joining P(x_1,y_1) and Q(x_2,y_2) is….

If the points (x_1,y_1), (x_2,y_2) and (x_1 + x_2, y_1+y_2) are collinear, prove that x_1y_2 = x_2y_1

If O be the origin and if P(x_1, y_1) and P_2 (x_2, y_2) are two points, the OP_1 (OP_2) sin angle P_1OP_2 , is equal to