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

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

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 ].

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

If is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then is unit vector if