Lesson 3.1 · 13 of 25 lessons
Dot products & orthogonality
Carry the right angle created by a dot product into projection and least-squares error.
Open the interactive animation01 · Story
What to verify in this scene
Follow the explanations and operations, then identify the mathematical evidence that remains in the final scene.
- 01
The dot product measures how much two vectors face the same direction
- 02
dot(u, v) = 0
The two vectors are orthogonal
02 · Notebook
The runnable notebook
This source creates the mathematical objects and controls the order of operations and animation. Read it here, then play the same scene yourself.
2d
zoom 1
coordinates on
2, 1 #u@
-1, 2 #v@
// The **dot product** measures how much two vectors face the same direction
focus u v
checkpoint Dot products & orthogonality
focus -
dot(u, v) #d@
// `dot({{u}}, {{v}}) = 0`\nThe two vectors are **orthogonal**
focus u v03 · Unit 3
Lessons in this unit
Orthogonality, projection & least squares — Carry the right angle created by a dot product into projection and least-squares error.