Q.

If A, B, C and D are position vectors a→,b→,c→ and d→, respectively, such that  a→−b→=2(d→−c→). Then

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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 is D.

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Detailed Solution

a→−b→=2(d→−c→)∴ a→+2c→2+1=b→+2d→2+1Hence, 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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If A, B, C and D are position vectors a→,b→,c→ and d→, respectively, such that  a→−b→=2(d→−c→). Then