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Question

^i×(a×^i)+^j×(a×^j)+^k×(a×^k) is always equal to

A
a
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B
a
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C
2a
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D
2a
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Solution

The correct option is C 2a
We have
^i×(a×^i)
=(^i.^i)a(a.^i)^i
=a(a.^i)^i

Similarly,
^j×(a×^j)
=a(a.^j)^j

^k×(a×^k)
=a(a.^k)^k

Now
^i×(a×^i)+^j×(a×^j)+^k×(a×^k)
=3a[(a.^i)^i+(a.^j)^j+(a.^k)^k]=2a

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