Find the coordinates of points Q and R on medians BE and CF respectively such that BQ:CF =2:1 and CR:RF =2:1​

Co-ordinates of points P and Q are -2 and 2 respectively. Find d(P,Q).

If AD, BE and CF are the altitudes of Delta ABC whose vertex A is (-4,5). The coordinates of points E and F are (4,1) and (-1,-4), respectively. Equation of BC is

Let C_1 and C_2 be parabolas x^2 = y - 1 and y^2 = x-1 respectively. Let P be any point on C_1 and Q be any point C_2 . Let P_1 and Q_1 be the reflection of P and Q, respectively w.r.t the line y = x then prove that P_1 lies on C_2 and Q_1 lies on C_1 and PQ >= [P P_1, Q Q_1] . Hence or otherwise , determine points P_0 and Q_0 on the parabolas C_1 and C_2 respectively such that P_0 Q_0 <= PQ for all pairs of points (P,Q) with P on C_1 and Q on C_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

AD is the median on BC. Find the coordinates of the point D

The centroid of a triangle ABC is at the point (1,1,1) . If the coordinates of A and B are (3,-5,7) and (-1,7,-6) , respectively, find the coordinates of the point C.

PQRS is a rhombus . Its diagonals PR and QS intersect at the point M and satisfy QS=2PR. If the coordinates of S and M are (1,1) and (2,-1) respectively , find the coordinates of P .

PQRS is a rhombus. Its diagonals PR and QS intersect at the points M and satisfy QS =2PR. If the coordinates of S and M are (1,1) and (2,-1) respectively , find the coordinates of P.

If the coordinates of the points A,B,C,D be (1,2,3),(4,5,7),(-4,3,-6) and (2,9,2) respectively , then find the angle between the line AB and CD.