Cross Product Review

The two main ways to find the cross products are using determinants/cofactors, and the quicker method without cofactors. In the determinants/cofactors method, you must use cofactor expansion where the values of the vectors are placed in a determinant and then expanded into cofactors for addition. An example can be seen below: 

Another method is by using the determinant also, but by using the quick method without cofactors, but by copying the first two columns to the right so one can multiply diagonally while adding or subtracting the values. You add when the multiplication is done from a top, left to a down, right while you subtract when it is from a down, left to a top, right. One can learn many things through the dot products such as how lluxvll equals the area of a parallelogram. Another important thing is the triple scalar product, which can only be found out when there are three vectors in space. The triple scalar product can be used to find the volume of the 3D shape the vector forms from one side. 
An example of the shortcut method can be seen below: