Question

What is the definition of the triple scalar product for vectors u, v and w in ${\mathrm{ℝ}}^3$?

Short answer

The triple scalar product is$u·(v\times w)=v·(w\times u)=w·(u\times v)$.

Step-by-step solution

Step 1. Given Information 

We have to define the definition of the triple scalar product for vectors u, v and w in ${\mathrm{ℝ}}^3$.

Step 2. The definition of the triple scalar product

Let u, v and w be three vectors in ${\mathrm{ℝ}}^3$. The triple scalar product is$u·(v\times w)=v·(w\times u)=w·(u\times v)$. The triple scalar product is the signed volume of the parallelepiped formed using the three vectors, u, v and w.