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Question

If a=^i+^j,b=^i+^k, then {{(a×b)×a}×a}×b=

A
^i+^j+^k
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B
2(^i+2^j^k)
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C
^i+^j+^k
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D
^i^j+^k
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Solution

The correct option is C 2(^i+2^j^k)
Firstly we have
(¯¯¯aׯ¯b)ׯ¯¯a
=a2¯¯b(¯¯¯a.¯¯b)¯¯¯a
=2¯i+2¯¯¯k¯i¯j
=¯i¯j+2¯¯¯k

Now, the result obtained above is cross producted with ¯¯¯a to get
(¯i¯j+2¯¯¯k)×(¯i+¯j)
=0+¯¯¯k+¯¯¯k+0+2¯j2¯i
=2¯i+2¯j+2¯¯¯k

The result obtained is cross producted with ¯¯b, to get (2¯i+2¯j+2¯¯¯k)×(¯i+¯¯¯k)
=0+2¯j2¯¯¯k+2¯i+2¯j+0
=2¯i+4¯j2¯¯¯k
So answer is option C

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