# parameterizing lines and planes

(2.3 hours to learn)

## Summary

Lines and planes can be defined either as spans of vectors or as solutions to systems of linear equations. Vector operations (in particular, dot products and cross products) allow us to convert between these representations. These tools also let us compute distances between points, lines, and planes.

## Context

This concept has the prerequisites:

- cross product (The cross product is needed to satisfy orthogonality constraints.)
- dot product (The dot product is used to define orthogonality constraints.)
- linear systems as matrices (Lines and planes can be represented in terms of linear systems.)

## Core resources (read/watch one of the following)

## See also

- These ideas can be extended to parameterize surfaces .