The position vectors of the points A, B and C are and respectively. Show that the points A, B and C are collinear.

Find the direction ratios and the direction cosines of the vector joining the points A(2, 1, -2) and B(3, 5, -4).

Show that the points A, B and C having position vectors and respectively, are collinear.

If the position vectors of the vertices A, B and C of a ∆ABC be and respectively, prove that ∆ABC is equilateral.

Show that the points A, B and C having position vectors and respectively, form the vertices of a right-angled triangle.