If the vertices A, B, C of ΔABC have position vectors (1, 2, 3),(-1, 0,0),(0, 1, 2) respectively, what is the magnitude of ∠ ABC?

Find the magnitude of two vectors and having the same magnitude and such that the angle between them is 60^o and their scalar product is 1/2.

Show that the points whose position vectors are form a right triangle.

If A, B, C have position vectors (0, 1, 1), (3, 1, 5), (0, 3, 3) respectively, show that is right angled at C.