A(5,4),B(3,8),C(-1,6) and D are coplanar points. Find the coordinates of D so that `vec AB= vec DC`.

Given four points A(2,2), B(2,4),C(1,2) and D(-1,3) . Find the point P that vec (AP)= vec (AB)+ vec (CD) .

Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the projection of vec(BC) on vec(AB) .

if A,B,C,D and E are five coplanar points, then vec(DA) + vec( DB) + vec(DC ) + vec( AE) + vec( BE) + vec( CE) is equal to :

If A,B,C and D are any four points in space prove that |quad vec (AB) xx vec (CD)+ vec (BC) xx vec (AD) + vec (CA) xx vec (BD)|=4(area of Delta ABC) .

Find the equation of a line passing through the points A(0, 6, -9) and B(-3,-6,3). If D is the foot of the perpendicular drawn from a point C(7,4,-1) on the line AB, then find the coordinates of the point D and the equation of line CD.

If ABC is triangle and D is the mid-point of [BC], prove that vec AB + vec AC= 2 vec AD .

A,B,C and D are four points with position vectors vec a , vec b , vec c and vec d respectively such that 5 vec a - 2 vec b + 6 vec c- 9 vec d= vec 0 . Show that the point A,B,C,D are coplanar and find find the P.V. of the point in which the lines AC and BD intersects.

ABCD is a parallelogram. If the points A , B and C are respectively : (1,2), (5,4),(3,8) Find the coordinates of the point D.

Let (4, 2), B (6, 5) and C (1, 4) be the vertices of triangleABC . :- The median from A meets BC at D. Find the coordinates of the point D.

ABCD is a parallelogram. If the points A , B and C are respectively : (2,3), (1,4),(1,-2) Find the coordinates of the point D.