---
title: "Dot and cross products"
weight: 4
---

**Author:** John Wellbelove  
**Date:** 2019  

## Dot Product
The dot product of two vectors is the sum of the products of the corresponding elements.  
The dot product of vectors `(x1, y1)` and `(x2, y2)` is `x1 * x2 + y1 * y2`.  
If `A` & `B` are vectors, the dot product is `|A||B|cos(θ)`, where `θ` is the angle between the `A` and `B`.  

`|A|` is the length of the vector `A`.  
`|B|` is the length of the vector `B`.  

Therefore, we can calculate `cos(θ) = (A ⋅ B)/(|A||B|)`.  
A dot product of `0` indicates two perpendicular lines, and the dot product is greatest when the lines are parallel.

## Cross Product

The cross product of vectors `(x1, y1)` and `(x2, y2)` is `x1 * y2 - y1 * x2`  
If `A` & `B` are vectors, the cross product is `|A||B|sin(θ)`.  
`|θ|` is the angle between the two vectors, but `θ` can be positive or negative.

Therefore, we can calculate `sin(θ) = (A x B)/(|A||B|)`.  