If A(2,-1,3), B(8,5,-6) and C(4,1,0) are the vertices of a triangle, show that |`vec AB| = 3 | vec AC|`

If A, B and C are the vertices of a triangle ABC, then what is the value of vec(AB) + vec(BC) + vec(CA) ?

A (8,0), B (0,-8) and C (-16, 0) are the vertices of a triangle ABC. If P is in AB and Q is in AC such that AP : PB = AQ : QC =3:5, show that 8PQ = 3 BC.

A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC. Find : the slope of the line parallel to AC.

A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC. Find : the slope of the altitude of AB.

If A(4,8,12), B(2,4,6), C(3,5,4) and D(5,8,5) are four points, show that the lines vec(AB) and vec(CD) intersect.

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 .

If A(2, 3, 4), B(5, 4, -1), C(3, 6, 2) and D(1, 2, 0) be four points, show that vec(AB) is perpendicular to vec(CD) .

The given points A, B, C are the vertices of a triangle. Determine the vectors vec(AB),vec(BC) and vec(CA) and the lengths of these vectors in the following case. A(8,6,1), B(2,0,1), C(-4,0,-5)

If D and E are the mid-points of sides AB and AC of a triangle A B C respectively, show that vec B E+ vec D C=3/2 vec B Cdot