A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). 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.