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Question

If a=^i+^j+^k,b=^i+^j^k,c=^i^j+^k and d=^i^j^k, then (a×b)×(c×d)=

A
0
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B
3^i5^j+7^k
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C
5^j8^k
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D
8^k
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Solution

The correct option is D 8^k
a×b
=(^i+^j+^k)×(^i+^j^k)
=2^i+2^j ...(i)
c×d
=(^i^j+^k)×(^i^j^k)
=2^i+2^j ...(ii)
Hence
(2^i+2^j)×(2^i+2^j)
=4^k4^k
=8^k

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