8. What were the important uses in the course of the dot product?
The cross product?
Answer
: The main application of the dot-product was in describing when two vectors were perpendicular: Two vectors are perpendicular if and only if their dot product is 0. This, in turn, was used to write the equation of a plane in terms of a normal and a point on the plane. It was also used in the derivation of the test used in the Lagrange multiplier method.The cross-product was used in constructing the normal to the plane defined by three points.