Examples
Examples
Try the starting example
- Source vector
- 3,4,0
- Nonzero target direction vector
- 1,0,0
- Parallel projection vector
- 3, 0, 0
- Orthogonal residual vector
- 0, 4, 0
- Signed length along target direction
- 3
- Orthogonal residual norm
- 4
Try another scenario
- Source vector
- 3,4,0
- Nonzero target direction vector
- 0,2,0
- Parallel projection vector
- 0, 4, 0
- Orthogonal residual vector
- 3, 0, 0
- Signed length along target direction
- 4
- Orthogonal residual norm
- 3
Calculation method
Calculation method
Parallel projection vector
Normalise the target vector, dot source with it, then multiply that signed length by the target unit vector.
Orthogonal residual vector
Source minus parallel projection.
Signed length along target direction
Source dot target unit vector; negative means opposite target direction.
Orthogonal residual norm
Euclidean norm of the orthogonal residual.
Symbols and units
- a
- Source vector
- b
- Nonzero target direction vector
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Projects one real Euclidean vector onto a nonzero direction of the same dimension. Input target magnitude does not affect the projection. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: orthogonal vector projection ↗
Background reading; this does not imply endorsement or independent review of SumFizz.