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The position of vectors of the points P and Q with respect to the origin O are a→=i^+3j^−2k^ and b→=3i^−j^−2k^ respectively. If M is a point on PQ ,such that OM is the bisector of ∠POQ, then OM→ is

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a

2(i^−j^+k^)

b

2i^+j^−2k^

c

2(−i^+j^−k^)

d

2(i^+j^+k^)

answer is B.

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Detailed Solution

Since |OP→|=|OQ→|=14,ΔOPQ is isosceles.Hence, the internal bisector OM is perpendicular to PQ and M is the midpoint of P and Q. Therefore,OM→=12 (OP→+OQ→)=2i^+j^−2k^

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