The correct option is C Null vector #160;i, #160;j,#160;k are 3 mutually perpendicular vectors such that #160;i×#160; j=k #160;j×#160;k=i ...

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Vector Addition

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Question

$^i \times (^j \times^k) +^j \times (^k \times^i) +^k \times (^i \times^j) =$

^i

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^j

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^k

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Null vector

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Solution

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

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