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Question

A vector c of magnitude 56 directed along the bisector of the angle between a=7ˆi4ˆj4ˆk and b=2ˆiˆj+2ˆk, is

A
±53(2ˆi+7ˆj+ˆk)
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B
±35(ˆi+7ˆj+2ˆk)
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C
±53(ˆi2ˆj+7ˆk)
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D
±53(ˆi7ˆj+2ˆk)
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Solution

The correct option is C ±53(ˆi7ˆj+2ˆk)
The angle bisectors will be sum and difference of the unit vectors of the two arms.

Thus, 7^i4^j4^k9±2^i^j+2^k3

=^i7^j+2^k9 or 15^i^j10^k9

We find the first direction in the options and since we need a vector of magnitude 56, we have ±53(^i7^j+2^k)

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