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Question

If a.b=1 and a×b=jk, where a=i+j+k, then b is

A
ij+k
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B
2jk
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C
i
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D
2i
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Solution

The correct option is C i
Let b=bxi+byj+bzk ¯a.¯b
=bx+by+bz
=1 ...(i)
¯aׯb =i(bzby)+j(bxbz)+k(bybx)
=jk

Therefore bz=by
bxbz=1

Substituting in (i)
bx+by+bz
=bx+2bz
=1+bz+2bz
=1+3bz
=1 ... from (i)

Hence bz=by=0
bx=1

Thus ¯b=i

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