**What is the geometric difference between a dot product and a cross product? Can you describe cross-products and dot products as determinants?**

Suppose you had two vectors (of any kind) and you wanted to determine how “much” of one the vectors was parallel to the other. The dot product is the mathematical operation between the two vectors that results in a number that quantifies how parallel the two vectors are. On the other hand, suppose you wanted to know the direction which is perpendicular to both of your two vectors. The cross product gives you an output vector that is mutually perpendicular to both of your input vectors, as long as your two input vectors are at least a little bit perpendicular to each other. A cross product can be written as a determinant but a dot product cannot.