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Solved: Scalar triple product Another operation with
Chapter 10, Problem 54E(choose chapter or problem)
54-56. Scalar triple product Another operation with vectors is the scalar triple product, defined to be \(\mathbf{u} \cdot(\mathbf{v} \times \mathbf{w})\), for vectors u, v, and w in \(\mathbf{R}^{3}\).
Express u, v, and w in terms of their components and show that \(\mathbf{u} \cdot(\mathbf{v} \times \mathbf{w})\) equals the determinant
\(\left|\begin{array}{lll} u_{1} & u_{2} & u_{3} \\ v_{1} & v_{2} & v_{3} \\ w_{1} & w_{2} & w_{3} \end{array}\right| \)
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QUESTION:
54-56. Scalar triple product Another operation with vectors is the scalar triple product, defined to be \(\mathbf{u} \cdot(\mathbf{v} \times \mathbf{w})\), for vectors u, v, and w in \(\mathbf{R}^{3}\).
Express u, v, and w in terms of their components and show that \(\mathbf{u} \cdot(\mathbf{v} \times \mathbf{w})\) equals the determinant
\(\left|\begin{array}{lll} u_{1} & u_{2} & u_{3} \\ v_{1} & v_{2} & v_{3} \\ w_{1} & w_{2} & w_{3} \end{array}\right| \)
ANSWER:Solution 54EStep 1 of 1:Scalar triple product is an operation with vectors defined