Module 1 : A Crash Course in Vectors
Lecture 1 : Scalar And Vector Fields
Scalar and Vector Triple Products
  One can form scalars and vectors from multiple vectors. Scalar and vector triple products are often useful.
The scalar triple product of vectors $\vec A, \vec B$ and $\vec C$ is defined by
 
\begin{displaymath}\vec A\cdot(\vec B\times\vec C)= \vec B\cdot(\vec C\times\vec A)= \vec C\cdot(\vec A\times\vec B)\end{displaymath}
  Note that the scalar triple product is the same for any cyclic permutation of the three vectors $\vec A, \vec B$ and $\vec C$. In terms of the cartesian components, the product can bew written as the determinant
 
  Since $\vec B\times\vec C$ gives the area of a parallelogram of sides $\vec B$ and $\vec C$, the triple product $\vec A\cdot(\vec B\times\vec C)$ gives the volume of a parallelopiped of sides $\vec A$, $\vec B$ and $\vec C$.
   
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