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Question

If a=4^i+4^j7^k, then the value of ^i×(a×^i)+^j×(a×^j)+^k×(a×^k)=

A
4^i+4^j7^k
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B
8^i+8^j14^k
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C
8^i8^j14^k
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D
4^i4^j7^k
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Solution

The correct option is D 8^i+8^j14^k
(i×(a×i))+(j×(a×j))+(k×(a×k))
=(a(i.i)i(a.i))+(a(j.j)i(a.j))+(a(k.ki)i(a.k))
=a+i(ax)+a+j(ay)+a+k(az)
=3a+iax+jay+kaz
=3a+a
=2a
=2(4i+4j7k)
=8i+8j14k

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