If A, B, C and D are position vectors a→,b→,c→ and d→, respectively, such that  a→−b→=2(d→−c→). Then

a→−b→=2(d→−c→)∴ a→+2c→2+1=b→+2d→2+1Hence, AC and.BD trisect each other as L.H.S. is the position vector of a point trisecting A an C, and R.H.S. that of B and D.