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Mechanical Engineering QUESTION #2535
Question 1
The scalar triple product \(\mathbf{A} \cdot (\mathbf{B} \times \mathbf{C})\) geometrically represents:
  • The magnitude of the vector \(\mathbf{B} \times \mathbf{C}\)
  • The volume of the parallelepiped formed by \(\mathbf{A}\), \(\mathbf{B}\), \(\mathbf{C}\)✔️
  • The area of the triangle formed by the three vectors
  • The dot product of \(\mathbf{B}\) and \(\mathbf{C}\) projected onto \(\mathbf{A}\)
Correct Answer Explanation
The scalar triple product \(\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})\) equals the volume of the parallelepiped whose three edges are represented by vectors \(\mathbf{A}\), \(\mathbf{B}\), and \(\mathbf{C}\). If the result is zero, the vectors are coplanar.