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

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$a$

$- a$

$- 2 a$

$2 a$

answer is C.

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Detailed Solution

$\begin{array}{rcl} (i \cdot a) i - a + (j \cdot a) j - a + (k \cdot a) j - a \\ a & = & xi + yj + zk \\ xi + yj + zk - 3 a & = & a - 3 a \\ = & - 2 a \end{array}$

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