Question: Given three vectors (mathbf{a}, mathbf{b}) and (mathbf{b}) show, making use of the representation with the determinant that: ((mathbf{a} times mathbf{b}) cdot mathbf{c}=mathbf{a} cdot(mathbf{b} times mathbf{c})=mathbf{b}

Given three vectors \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{b}\) show, making use of the representation with the determinant that: \((\mathbf{a} \times \mathbf{b}) \cdot \mathbf{c}=\mathbf{a} \cdot(\mathbf{b} \times \mathbf{c})=\mathbf{b} \cdot(\mathbf{a} \times \mathbf{c})\). If not, the definition of parallelepiped volume would have been problematic.

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