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

Find the direction ratios and direction cosines of the vector

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

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

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