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Mechanical Engineering QUESTION #2554
Question 1
For two vectors \(\mathbf{A}\) and \(\mathbf{B}\), the vector triple product \(\mathbf{A}\times(\mathbf{B}\times\mathbf{C})\) equals:
  • \((\mathbf{A}\cdot\mathbf{C})\mathbf{B}-(\mathbf{A}\cdot\mathbf{B})\mathbf{C}\)✔️
  • \((\mathbf{A}\cdot\mathbf{B})\mathbf{C}-(\mathbf{A}\cdot\mathbf{C})\mathbf{B}\)
  • \((\mathbf{B}\cdot\mathbf{C})\mathbf{A}-(\mathbf{A}\cdot\mathbf{C})\mathbf{B}\)
  • \(\mathbf{B}(\mathbf{A}\cdot\mathbf{C})+\mathbf{C}(\mathbf{A}\cdot\mathbf{B})\)
Correct Answer Explanation
The BAC-CAB rule for the vector triple product: \(\mathbf{A}\times(\mathbf{B}\times\mathbf{C})=\mathbf{B}(\mathbf{A}\cdot\mathbf{C})-\mathbf{C}(\mathbf{A}\cdot\mathbf{B})\). The result lies in the plane of \(\mathbf{B}\) and \(\mathbf{C}\).