If are unit vectors such that find the value of

Show that is perpendicular to for any two nonzero vectors .

If and then what can be concluded about the vector

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 ].