The Cross Product of Two Vectors

The cross product of two vectors is a vector that is perpendicular to both. The easiest way to find it is to use matrices, but you can also use this formula:

To find the cross product by using a matrix, create a 3x3 matrix. The first row should be the variables i, j, and k. The second row should be the values of the first vector, and the third row should be the values of the second vector.

For example, this is what the matrix would look like when finding the cross product of the vectors <1, 2, 1> and <3, 1, 2>:

i j k

1 2 1

3 1 2

Now, find the discriminant of this matrix:

Finally, we see that the cross product of these two vectors is <3, 1, -5>.