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The scalar triple product \( \mathbf{A} \cdot (\mathbf{B} \times \mathbf{C}) \) represents

  • A.the sum of the three individual magnitudes of the vectors
  • B.the volume of the parallelepiped formed by the three vectors
  • C.the surface area of the parallelepiped formed by the three vectors
  • D.a vector lying in the plane of the second and third vectors

Answer: B

The cross product gives the base area and the dot product projects the third vector onto the normal to that base, giving base times height. The product is unchanged by a cyclic permutation of the three vectors, and it vanishes when they are coplanar.

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