If the position vectors of the vertices
A, B and C of a ∆ABC be (1, 2, 3), ( - 1, 0, 0) and (0, 1, 2) respectively then find ∠ABC.

Show that the vectors and form a right - angled triangle.

Three vertices of a triangle are A(0, - 1, - 2), B(3, 1, 4) and C(5, 7, 1). Show that it is a right - angled triangle. Also, find its other two angles.

If and are two unit vectors such that find

If and are two vectors such that then prove that vector is perpendicular to the vector