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 A(x_(1),y_(1))andB(x_(2),y_(2)) subtends an angle alpha at the origin O, then find the value of cosalpha .

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 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

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))

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

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

If point P divided line segment joining points A(x_1,y_1,z_1) and B(x_2,y_2,z_2) in ratio k : 1 then co - ordinates on P.

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)

Slope of the line that passes through the points P(x_(1),y_(1)) and Q(X_(2),y_(2)) and making an angle theta with X-axis is

If R(x,y) is a point on the line segment joining the points P(a,b) and Q(b,a), then prove that x+y=a+b