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A, B, C and D have position vectors veca...

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

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The correct Answer is:
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.
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