What are some uses for the vector triple product in computer graphics?

I have just learned about the vector triple product (Lagrange formula) from a math for computer graphics textbook, however the book does not mention any use cases for it beyond the fact that it's a simpler way to say:

   cross(a,cross(b,c) == b*(dot(a,c))-c*(dot(a,b)


Why is this emphasized? Is it because it's simpler to read?

• Well its useful to calculate volumes of paralell epipeds and by extension tetrahedra. So basically the volume of any polygon bound object. Which in turn is useful for making uniform random point clouds. – joojaa May 16 '20 at 21:46
• Ive heard that argument for the scalar triple product, but here im asking about the vector triple product though. I dont think you can calculate the volune of parallelepipeds using the vector triple product – mbl May 17 '20 at 1:17