Prove that $\to a \times (\to b \times \to c) + \to b \times (\to c \times \to a) + \to c \times (\to a \times \to b) = 0$

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Solution

$\begin{matrix} \to a \times (\to b \times \to c) + \to b \times (\to c \times \to a) + \to c (\to a \times \to b) = (\to a \cdot \to c) \to b - (\to a \cdot \to b) \to c + (\to b \cdot \to a) \to c - (\to b \cdot \to c) \to a + (\to c \cdot \to b) \to a - (\to c \cdot \to a) \to b = (\to a \cdot \to b) \to c - (\to a \cdot \to b) \to c + (\to b \cdot \to c) \to a - (\to b \cdot \to c) \to a + (\to c \cdot \to a) \to b - (\to c \cdot \to a) \to b = 0 \end{matrix}$

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