Vector dot and cross products

In this tutorial, we define two ways to "multiply" vectors-- the dot product and the cross product. As we progress, we'll get an intuitive feel for their meaning, how they can used and how the two vector products relate to each other.

Vector dot product and vector length

Proving vector dot product properties

Proof of the Cauchy-Schwarz inequality

Vector triangle inequality

Defining the angle between vectors

Defining a plane in R3 with a point and normal vector

Cross product introduction

Proof: Relationship between cross product and sin of angle

Dot and cross product comparison/intuition

Vector triple product expansion (very optional)

Normal vector from plane equation

Point distance to plane

Distance between planes