Question

If vector (a, b, c) are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is (1/2)vector|a x b + b x c + c x a|. Also deduce the condition for collinearity of the points A, B, C

Answer 1

If the points A, B, C are collinear, then the area of ∆ABC = 0.

Thus vector|a x b + b x c + c x a| = 0 vector is the required condition of collinearity of the points with position a, b, c.