Equations · equation
Dot Product
Vectors & Geometry · 1881
- Equation
- a · b = |a| |b| cos θ = a_x b_x + a_y b_y + a_z b_z
- Field
- Vectors & Geometry
- Symbols
- a, b two vectors · θ the angle between them · a · b a number, not a vector: how much of one lies along the other
- Year
- 1881
Significance
The overlap of two directions. Zero when they are perpendicular, largest when aligned, negative when opposed — which is why work is F · d and not F times d: a force at right angles to the motion does nothing. The component form on the right is what a computer calculates; the cosine form is what it means.
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.