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

If A(2, 3, 4), B(5, 4, - 1), C(3, 6, 2) and D(1, 2, 0) be four points, show that is perpendicular to

Find the value of λ for which the vectors and are perpendicular to each other.

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 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.