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Question

^i×(^j×^k)+^j×(^k×^i)+^k×(^i×^j)=

A
^i
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B
^j
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C
^k
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D
Null vector
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Solution

The correct option is C Null vector
^i,^j,^k are 3 mutually perpendicular vectors such that
^i×^j=k
^j×^k=i
^k×^i=j.
Hence
^i×(^j×^k)+^j×(^k×^i)+^k×(^i×^j)
=^i×(^i)+^j×(^j)+^k×(^k)
=0

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