P,Q have position vectors →a & →b relative to the origin 'O' and X,Y divide →PQ intermally and extemally respectively in the ratio 2:1, then vector →XY=
A
32(→b−→a)
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B
43(→c−→a)
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C
56(→b−→a)
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D
43(→b−→a)
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Solution
The correct option is D43(→b−→a) X divides →PQ internally in 2:1. Thus, →X=→a+2→b2+1 Y divides →PQ externally in 2:1. Thus, →Y=2→b−→a2−1 →X=→a+2→b3 and →Y=2→b−→a ∴→XY=→Y−→X=6→b−3→a−→a−2→b3 →XY=4→b−4→a3