Using property of scalar triple product, prove that $(¯ a + ¯ b + ¯ c) \times (¯ b - ¯ a) \cdot ¯ c = 2 ¯ a \cdot ¯ b \times ¯ c$ .

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Solution

$\begin{matrix} (\to a + \to b + \to c) \times (\to b - \to a) . \to c (\to a \times \to b + \to a \times \to b - \to c \times \to a) . \to c = 2 \to a \times \to b . \to c = 2 \to a . (\to b \times \to c) = 2 [\to a \to b \to c] \end{matrix}$

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