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Question

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

A
24(^i+^j2^k)
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B
24(^i^j^k)
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C
12(2^i+^j3^k)
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D
12(^i2^j+3^k)
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Solution

The correct option is C 24(^i+^j2^k)
¯¯¯aׯ¯b
=(2¯i+¯j+3¯¯¯k)×(3¯i+2¯j+¯¯¯k)
=5¯i+7¯j+¯¯¯k ...(i)

¯¯cׯ¯¯d
=(¯i¯j4¯¯¯k)×(¯i+2¯j¯¯¯k)
=9¯i3¯j+3¯¯¯k ...(ii)

(5¯i+7¯j+¯¯¯k)×(9¯i3¯j+3¯¯¯k)
=24¯i+24¯j48¯¯¯k
=24(¯i+¯j2¯¯¯k)

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