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 lines AB and CD.

The coordinates of the points A,B,C and D are (-2,3), (8,9), (0,4) and (3,0) respectively . Find the ratio in which the line -segment overline(AB) is divided by the line -segment overline(CD) .

Let A(-2, 0, 3), B(0, 3, -3), C(3, 3, 5) and D(5, 4, 3) be four given points, find the acute angle between the lines AB and CD.

The sides of the rectangle ABCD are parallel to the coordinate axis. If the coordinates of the vertices B and D be (7,3) and (2,6) respectively, find the coordinates of the vertices A and C .

If A, B, C, D are the points (2, 3, -1), (5, 2, 3), (4, 3, -5) and (-2, 1, -8) respectively, then find the projection of AB on CD.

The sides of the rectangle ABCD are parallel to the coordinate axes. If the coordinates of the vertices B and D be (7,3) and (2,6) respectively , find the coordinates of the vertices A and C .

The coordinates of the points A,B,C are (-2,1),(-1,-3) and (3,-2) respectively . Show that , AB =BC and angleABC is a right angle If D is the fourth vertex of the square ABCD , find the coordinates of D and also find the point of intersection of diagonals of ABCD.

A, B, C, D are consecutive vertices of a parallelogram. If the coordinates of A, B and C are (0, 0, 0), (3, -4, 4) and (7, 1, 4) respectively, find using direction ratios the coordinates of the vertex D.

If the point C(x,y,-14) lies on the line -segment bar(AB) produced where the coordinates of A and B are (2,-3,4) and (3,1,-2) respectively, then find the values of x and y.

If the point C( x , y , -14) lies on the line-segment overline(AB) produced where the coordinates of A and B are ( 2 , - 3 , 4) and ( 3 , 1 , -2) respectively , then find te values of x and y .

The coordinates of the points A and B are (2,4) and (2,6) respectively . The point P is on that side of AB opposite to the origin . If PAB be an equilateral triangle , find the coordinates of P.