Mathegoras

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Dot product with a cross product of differences

High school · ●●○○○ 20 pts

Let a=(−3101)\mathbf{a} = \begin{pmatrix} -3 \\ 10 \\ 1 \end{pmatrix}, b=(5π0)\mathbf{b} = \begin{pmatrix} 5 \\ \pi \\ 0 \end{pmatrix}, and c=(−2−27)\mathbf{c} = \begin{pmatrix} -2 \\ -2 \\ 7 \end{pmatrix}. Compute (a−b)⋅[(b−c)×(c−a)](\mathbf{a} - \mathbf{b}) \cdot [(\mathbf{b} - \mathbf{c}) \times (\mathbf{c} - \mathbf{a})].

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scalar triple productcross productvector algebra