If 'alpha' be the angle subtended by the points `P(x_1, y_1) and Q(x_2, y_2)` at origin O, Show that `OP.OQ.cos alpha= x_1x_2 + y_1y_2`.

If 'alpha' be the angle subtended by the points P(x_(1),y_(1)) and Q(x_(2),y_(2)) at origin O, Show that OP.OQ.cos alpha=x_(1)x_(2)+y_(1)y_(2)

If the line segment joining the points P(x_1, y_1)a n d\ Q(x_2, y_2) subtends an angle alpha at the origin O, prove that : O PdotO Q\ cosalpha=x_1x_2+y_1y_2dot

If the line segment joining the points P(x_1, y_1)a n d Q(x_2, y_2) subtends an angle alpha at the origin O, prove that : O PdotO Q cosalpha=x_1x_2+y_1y_2dot

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

If theta\ is the angle which the straight line joining the points (x_1, y_1)a n d\ (x_2, y_2) subtends at the origin, prove that tantheta=(x_2y_1-x_1y_2)/(x_1x_2+y_1y_2)\ a n dcostheta=(x_1x_2+y_1y_2)/(sqrt(x1 2+y1 2x2 2+y2 2))

If theta\ is the angle which the straight line joining the points (x_1, y_1)a n d\ (x_2, y_2) subtends at the origin, prove that tantheta=(x_2y_1-x_1y_2)/(x_1x_2+y_1y_2)\ a n dcostheta=(x_1x_2+y_1y_2)/(sqrt(x1 2 x2 2+y2 2x1 2+y1 2x2 2+ y1 2y2 2))

Three points P (h, k), Q(x_1, y_1) and R (x_2,y_2) lie on a line. Show that : (h-x_1)(y_2-y_1)= (k-y_1)(x_2-x_1) .

If the points P(h,k),Q(X_1,Y_1) and R(X_2,Y_2) lie on a line.Show that (h-x_1)(y_2-y_1)=(k-y_1)(x_2-x_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

If the line joining the points (_x_1, y_1) and (x_2, y_2) subtends a right angle at the point (1,1), then x_1 + x_2 + y_2 + y_2 is equal to