The preceding section looked at one way to “multiply” vectors—the dot product. This section examines the cross product. The biggest difference between the two is that the dot product returns a scalar value and the cross product returns another vector. Let's look at the method for calculating the cross product.
Some math texts refer to the cross product of two vectors as the vector product because that is what the cross product returns.
A × B = [(a2b3 – a3b2) (a3b1 – a1b3) (a1b2 – a2b1)]
for any two vectors A = [a1 a2 a3] and B = [b1 b2 b3].
Example 4.15: Cross Product
Find the cross product of vectors A = [5 –6 0] and B = [1 2 3].
The cross product returns another vector, so you can calculate each component ...