You can think of the dot product as the product of the magnitudes of two vectors multiplied by the cosine of the angle between them. A common use of the dot product is to find the volume of an object formed by gliding the interior of a plane figure along a vector. If vector a is normal to the plane containing the figure and its length is the area of the figure, and then the figure is glided along vector b to form a solid, then the volume of the solid is $ a\centerdot b. $

A common application of this fact is the formula for the volume of a parallelipiped formed by vectors a, b, and c, which is the so-called "triple product", $ a\centerdot \left(b\times c\right). $