Equations · equation
Vector Projection
Vectors & Geometry · 1881
- Equation
- proj_b a = (a · b / |b|²) b, |proj_b a| = |a| cos θ
- Field
- Vectors & Geometry
- Symbols
- a the vector being projected · b the direction projected onto · proj_b a the shadow a casts along b
- Year
- 1881
Significance
How much of a force acts along a slope, how much of a velocity is toward the observer, how much of a field crosses a surface — every 'component along' in physics is a projection, and the dot product does the work. The redshift a spectrograph measures is the projection of a galaxy's velocity onto the line of sight; the rest is invisible to it.
Referenced by
equation
skill
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.