Question

A, B, C and D have position vectors `veca, vecb, vecc and vecd`, repectively, such that `veca-vecb = 2(vecd-vecc)`. Then
A. AB and CD bisect each other
B. BD and AC bisect each other
C. AB and CD trisect each other
D. BD and AC trisect each other

Answer 1

Correct Answer - D
`veca-vecb= 2(vecd-vecc)`
`therefore (veca+ 2vecc)/(2+1) = (vecb+ 2vecd)/(2+1)` ltBrgt Hence, 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.