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.

If and are such that is perpendicular to then find the value of λ.

Find the angles of a triangle whose vertices are A(0, -1, -2), B(3, 1, 4) and C(5, 7, 1).

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

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?