In previous lessons, we've discussed geometric objects and ideas as largely static things. We've calculated distance, volume, area, angles, and equations at given moments in time. Even if these objects are moving, we have only dealt with them at one instant, performing calculations which disregard all information except the properties that describe them at one particular instant. While these kinds of calculations are useful, we have not yet been able to capture quantities that rely on more than one descriptor. For example, we can describe an object's speed with a single number, but to describe its velocity, we also need to know the direction it's moving in. We call speed a scalar and velocity a vector for this reason.

Vectors are very useful when describing real-world phenomena. It can be hard to visualize complex three dimensional equations, and vectors are one way mathematicians use to make it easier for themselves. They enable us to understand geometry in three-dimensional space, as well as to describe direction and displacement of points, and determine angles and lengths in situations that are too complicated to visualize.