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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

Text Solution

Verified by Experts

The correct Answer is:
D
`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.
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