If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC, [∠ABC is the angle between the vectors ].

If are unit vectors such that find the value of

If either vector then But the converse need not be true. Justify your answer with an example.

Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.

Show that the vectors form the vertices of a right angled triangle.