In the traditional approach to the teaching of vectors, the scalar product of two vectors u, v is usually defined to be

|u| . |v| . cos θ

where θ is defined to be the angle between the two vectors. In a similar way, the vector product of two vectors is defined to be a vector that makes a right handed triple with u and v, and whose length is given by

|u| . |v| . sin θ

From these definitions the familiar co-ordinate expressions for dot and cross products are derived.