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 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_(1)OP_(2)=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 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))

Find the distance between the points P(x_(1),y_(1),z_(1)) and Q(x_(2),y_(2),z_(2))

Find the distance between points P(x_1, y_1) and Q(x_2, y_2) : PQ is parallel to y-axis

Find the distance between points P(x_1, y_1) and Q(x_2, y_2) : PQ is parallel to x-axis

If O be the origin and P(2,3,4) and Q(1,-2,1) be any two points,show that OPOQ.

If [[x-y,2x-x_1],[2x-y,3x+y_1]], =[[-1,5],[0,13]] and coordinats of points P and Q be (x,y) and (x_1,y_1) respectively then P,Q=?