Equations · equation
Cross Product
Vectors & Geometry · 1881
- Equation
- |a × b| = |a| |b| sin θ, direction ⊥ to both by the right-hand rule
- Field
- Vectors & Geometry
- Year
- 1881
Symbols
a, b two vectors · θ the angle between them · a × b a third vector, perpendicular to the plane of the first two, with the area of their parallelogram as its length
Significance
The turning quantity. Torque is r × F, angular momentum r × p, the magnetic force qv × B — every time a physical effect points at right angles to its causes, this is the operation. Largest when the two are perpendicular and zero when parallel, which is why pushing straight along a wrench handle turns nothing. Its components are a determinant.
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