The cross product
In space, you need a way to describe how a plane is "tilting," or its inclination. You accomplish this by multiplying two vectors together to get a third vector perpendicular to the plane of the the two vectors. The direction of this vector tells you the inclination of the plane. This vector product is called the cross product.
The cross product of vectors and , denoted , is another vector perpendicular to both and , and whose length is equal to the product of the lengths of and and the sine of the angle between and . From geometry, the length is numerically equal to the area of the parallelogram formed by the two vectors.
Developed for use with Thomas' Calculus, published by Pearson.