The Cross Product

There are two types of vectors multiplication: dot product and cross product. The cross product of two vectors u and v is defined as
 

where n is a unit normal vector that is perpendicular to both u and v. In other word, u x v is always perpendicular to both u and v. Take note that the direction of u x v adhere to the right hand grip rule. 

The graph below shows the vectors u, v and u x v. Try to move points A and B and observe the changes of the vector u x v. Then, do the same thing by moving the meeting point of vectors u and v.

According to the definition, the length of u x v depends on the angle between the vectors u and v. Somehow, when it comes to calculation of u x v, the determinant formula is used. Take a look at the video below to learn about it.

Betty, Created with GeoGebra, Screencast-O-Matic and Thomas Calculus, Pearson.