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The vector triple product identity states that \( \mathbf{A} \times (\mathbf{B} \times \mathbf{C}) \) equals

  • A.\( \mathbf{A}(\mathbf{B} \cdot \mathbf{C}) - \mathbf{B}(\mathbf{A} \cdot \mathbf{C}) \)
  • B.\( (\mathbf{A} \times \mathbf{B}) \times \mathbf{C} \)
  • C.\( \mathbf{B}(\mathbf{A} \cdot \mathbf{C}) - \mathbf{C}(\mathbf{A} \cdot \mathbf{B}) \)
  • D.\( \mathbf{C}(\mathbf{A} \cdot \mathbf{B}) - \mathbf{B}(\mathbf{A} \cdot \mathbf{C}) \)

Answer: C

The mnemonic is that the result is the middle vector times the dot of the outer two, minus the last vector times the dot of the first two. The product is not associative, so the brackets cannot be moved without changing the answer.

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