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Question Number 55948 by Tawa1 last updated on 06/Mar/19

	Answered by kaivan.ahmadi last updated on 07/Mar/19

	$a . A \times B = \| \begin{matrix} i j k \\ 3 - 1 2 \\ 2 1 - 1 \end{matrix} \| \| \begin{matrix} i j k \\ 3 - 1 2 \\ 2 1 - 1 \end{matrix} \| =$ $(i + 4 j + 3 k) - (- 2 k - 3 j + 2 i) = - 3 i + 7 j + 5 k$ $(A \times B) \times C = \| \begin{matrix} i j k \\ - 3 7 5 \\ 1 - 2 2 \end{matrix} \| \| \begin{matrix} i j k \\ - 3 7 5 \\ 1 - 2 2 \end{matrix} \| =$ $(14 i + 5 j + 6 k) - (7 k - 6 j - 10 i) =$ $24 i + 11 j - k$ $b . B \times C = \| \begin{matrix} i j k \\ 2 1 - 1 \\ 1 - 2 2 \end{matrix} \| \| \begin{matrix} i j k \\ 2 1 - 1 \\ 1 - 2 2 \end{matrix} \| =$ $(2 i - j - 4 k) - (k + 4 j + 2 i) =$ $- 5 j - 5 k$ $A \times (B \times C) = \| \begin{matrix} i j k \\ 3 - 1 2 \\ 0 - 5 - 5 \end{matrix} \| \| \begin{matrix} i j k \\ 3 - 1 2 \\ 0 - 5 - 5 \end{matrix} \| =$ $(5 i - 15 k) - (- 15 j - 10 i) =$ $15 i + 15 j - 15 k = 15 (i + j - k)$
	Commented by Tawa1 last updated on 07/Mar/19

	$God bless you sir$
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