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Question

If a=2^i+^j+2^k, then the value of ^i×(a×^i)2+^j×(a×^j)2+^k×(a×^k)2 is equal to

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Solution

^i×(a×^i)2
=(^i^i)a(a^i)^i2
=a2^i2
=^j+2^k2
=5
Similarly,
^j×(a×^j)2
=a^j2
=2^i+2^k2
=8
and ^k×(a×^k)2
=a2^k2
=2^i+^j2
=5
Now,
^i×(a×^i)2+^j×(a×^j)2+^k×(a×^k)2
=5+8+5=18

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