Projection changes with direction
Why is the projection residual perpendicular?
Interactive example
- Residual · direction
- 0
- Projection scale
- 3
The residual dot product is zero up to arithmetic precision.
See the values
| Object | x | y |
|---|---|---|
| Vector b | 3 | 2 |
| Projection | 3 | 0 |
| Residual | 0 | 2 |
What to notice
Compare a projection with its perpendicular residual.
Conditions
Real two-dimensional vectors; the direction is (1, t), so it is never zero.
What this example cannot show
This is one fixed vector and a two-dimensional illustration, not a general proof.
Sources and context
These sources provide topic context. The values and interaction are authored by AXIOVUM; no institutional endorsement is implied.