a×[a×(a×b)] is equal to :

=a×[(a⋅b)a−(a⋅a)b]=(a⋅b)(a×a)−(a⋅a)(a×b)=(a⋅b)0+(a⋅a)(b×a)=(a⋅a)(b×a)

a×[a×(a×b)] is equal to :

=a×[(a⋅b)a−(a⋅a)b]=(a⋅b)(a×a)−(a⋅a)(a×b)=(a⋅b)0+(a⋅a)(b×a)=(a⋅a)(b×a)

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$a \times [a \times (a \times b)]$ is equal to :

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$(a \times a) \cdot (b \times a)$

$[a \cdot (a \times b)] a$

$a \cdot (b \times a) - b \cdot (a \times b)$

$(a \cdot a) (b \times a)$

answer is D.

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Detailed Solution

$\begin{array}{l} = a \times [(a \cdot b) a - (a \cdot a) b] \\ = (a \cdot b) (a \times a) - (a \cdot a) (a \times b) \\ = (a \cdot b) 0 + (a \cdot a) (b \times a) = (a \cdot a) (b \times a) \end{array}$

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a×[a×(a×b)] is equal to :

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$a \times [a \times (a \times b)]$ is equal to :