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Question

If 4^i+7^j+8^k,2^i+3^j+4^k and 2^i+5^j+7^k are the position vectors of the vertices A, B and C respectively of triangle ABC. The position vector of the point where the bisector of angle A meets BC is

A
23(6^i8^j6^k)
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B
23(6^i+8^j+6^k)
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C
13(6^i+13^j+18^k)
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D
13(5^i+12^k)
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Solution

The correct option is C 13(6^i+13^j+18^k)
Suppose the bisector of angle A meets BC at D. Then, AD divides BC in the ratio AB : AC.
So, PV of D
=|AB|(2^i+5^j+7^k)+|AC|(2^i+3^j+4^k)|AB|+AC
But, AB=2^i4^j4^k
and AC=2^i2^j^k|AB|=6 and |AC|=3
pv of D=6(2^i+5^j+7^k)+3(2^i+3^j+4^k)6+3=13(6^i+13^j+18^k)

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