A, B, C and D have position vectors `veca, vecb, vecc and vecd`, repectively, such that `veca-vecb = 2(vecd-vecc)`. Then

Options

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

D

Explanation

`a-b=2(d-c)`
`therefore(a+2c)/(2+1)=(b+2d)/(2+1)`
Hence, AC and BD trisect each other as LHS is the position vector of a point trisecting A an C, and RHS that of B and D.