alleryWhich expression correctly represents the vector triple product $\mathbf{A}\times(\mathbf{B}\times\mathbf{C})$?
A$(\mathbf{A}\cdot\mathbf{B})\mathbf{C}-(\mathbf{A}\cdot\mathbf{C})\mathbf{B}$
B$(\mathbf{B}\cdot\mathbf{C})\mathbf{A}-(\mathbf{A}\cdot\mathbf{C})\mathbf{B}$
C$(\mathbf{A}\cdot\mathbf{C})\mathbf{B}-(\mathbf{A}\cdot\mathbf{B})\mathbf{C}$
D$(\mathbf{A}\times\mathbf{B})\cdot\mathbf{C}$
Answer & Solution
Correct answer: C. $(\mathbf{A}\cdot\mathbf{C})\mathbf{B}-(\mathbf{A}\cdot\mathbf{B})\mathbf{C}$
The standard identity is $\mathbf{A}\times(\mathbf{B}\times\mathbf{C})=(\mathbf{A}\cdot\mathbf{C})\mathbf{B}-(\mathbf{A}\cdot\mathbf{B})\mathbf{C}$.
This is often remembered as the BAC-CAB rule.
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