A, B have position vectors →a,→b relative to the origin O and X, Y divide −−→AB internally and externally respectively in the ratio 2 : 1. Then,−−→XY is equal to
A
32(→b−→a)
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B
43(→a−→b)
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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) Since X and Y divide −−→AB internally and externally in the ratio 2 : 1, therefore the position vectors of X and Y are given by 2→b+→a3 and 2→b−→a respectively. Thus, −−→XY=(2→b−→a)−13(2→b+→a)=43(→b−→a)