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Question

If a vector r of magnitude 36 is directed along the bisector of the angle between the vectors a=7ˆi4ˆj4ˆk and b=2ˆiˆj+2ˆk then r=

A
(ˆi7ˆj+2ˆk)
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B
(ˆi+7ˆj2ˆk)
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C
(ˆi+7ˆj+2ˆk)
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D
(ˆi7ˆj2ˆk)
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Solution

The correct option is B (ˆi7ˆj+2ˆk)
Given

a=7^i4^j4^k
b=2^i^j+2^k
angle bisector
c=ba+|a|b
c=((2)2+(1)2+22)(7^i4^j4^k)+((7)2+(4)2+(4)2)(2^i^j+2^k)
c=21^i12^j12^k18^i9^j+18^k
c=3^i21^j+6^k
unit vector of c
^c=3^i2^j+6^k96
r=magnitude×unitvector
r=36(3^i2^j+6^k96)
r=^i7^j+2^k

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