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Question

If a=2^i+^j+3^k, b=3^i+2^j+^k, c=^i^j4^k and d=^i+2^j^k, then (a×b)×(c×d)=

A
8(^i+^j+^k)
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B
16(^i^j+2^k)
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C
24(^i+^j2^k)
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D
12(^i+^j+^k)
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Solution

The correct option is C 24(^i+^j2^k)
We know,
(a×b)×(c×d)=[abd]c[abc]d=∣ ∣213321121∣ ∣c∣ ∣213321114∣ ∣d=8(^i^j4^k)+16(^i+2^j^k)=24^i+24^j48^k=24(^i+^j2^k)

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