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This semester I was asked to lecture Calculus 2 at the university in which I work. I gladly accepted

Anyway, we are up to the second module, which is Vectors. Today's lecture was about Scalar Triple Products and Vector Triple Products. My class is very attentive and was asking a lot of questions today. Unfortunately, the lecture notes I inherited had ZERO information on why we would need to evaluate a vector triple product, though it said there are numerous applications including mathematical modelling of particle and fluid dynamics. Scalar triple products are easy - we use them to evaluate the volume of a paralleliped and to determine if vectors or points are coplanar. Among the participation from the students, I was asked why we would need to evaluate the vector triple product, and for the life of me I could not think of a single application. I even checked Google and could not find one there either, although geometrically we can use the vector triple product to find a vector that lies in the same plane as the final two vectors.

Just to be clear, I'm talking about [tex]\displaystyle \mathbf{a} \times \left( \mathbf{b} \times \mathbf{c} \right) [/tex], which can be evaluated more easily using [tex]\displaystyle \left( \mathbf{a} \cdot \mathbf{c} \right) \mathbf{b} - \left( \mathbf{a} \cdot \mathbf{b} \right) \mathbf{c} [/tex].

So my question is, could somebody please give me some real-world examples of applications of the vector triple product? Thanks