Arrow keys move:
Grid:
Stretch an arrow, watch the needle stay put
a = b =
a · b (dot product)
‖a‖
‖b‖
cos θ = a · b / (‖a‖ ‖b‖)
angle θ
Unit vectors: â · b̂
Lesson examples
Pick an example, then drag.
What to try
- Keep a fixed and swing b once around it. Where does the needle cross 0? Where does it hit −1?
- Press b × 2 a few times. a · b and ‖b‖ grow, cos θ does not.
- Find two whole-number arrows with cos θ exactly 0 that are not on the axes.
- Load "Short vs long article". The tips are far apart, yet the score is exactly 1.
- Tick "lock directions" and drag a tip: only the length changes, the dial never moves.