Examples

The definition of the cross product can also be represented by the determinant of a matrix:




From the first three elements on the first row draw three diagonals to the right (e.g. the first diagonal would contain i, a2, and b3), and from the last three elements on the first row draw three diagonals to the left (e.g. the first diagonal would contain i, a3, and b2). Then multiply the elements on each of these six diagonals, and negate the last three products. The cross product would be defined by the sum of these products:



Next: The Derivative