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 [i]cross product[/i].[br][br]The cross product of vectors [math]\mathbf{v}[/math] and [math]\mathbf{u}[/math], denoted [math]\mathbf{v}\times\mathbf{u}[/math], is another vector perpendicular to both [math]\mathbf{v}[/math] and [math]\mathbf{u}[/math], and whose length is equal to the product of the lengths of [math]\mathbf{v}[/math] and [math]\mathbf{u}[/math] and the sine of the angle between [math]\mathbf{v}[/math] and [math]\mathbf{u}[/math]. From geometry, the length is numerically equal to the area of the parallelogram formed by the two vectors.

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]