alleryWhich identity for the scalar triple product is correct?
A$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})=\mathbf{A}\cdot(\mathbf{C}\times\mathbf{B})$
B$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})=\mathbf{B}\cdot(\mathbf{C}\times\mathbf{A})$
C$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})=(\mathbf{A}\cdot\mathbf{B})\times\mathbf{C}$
D$\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})=\mathbf{A}\times(\mathbf{B}\cdot\mathbf{C})$
Answer & Solution
Correct answer: B. $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})=\mathbf{B}\cdot(\mathbf{C}\times\mathbf{A})$
**The scalar triple product is cyclic:** $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})=\mathbf{B}\cdot(\mathbf{C}\times\mathbf{A})=\mathbf{C}\cdot(\mathbf{A}\times\mathbf{B})$.
Swapping two vectors changes the sign, so option A is not correct.
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