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- Vector_area abstract "In geometry, for a finite planar surface of scalar area , the vector area is defined as a vector whose magnitude is and whose direction is perpendicular to the plane, as determined by the right hand rule on the rim (moving one's right hand counterclockwise around the rim, when the palm of the hand is "touching" the surface, and the straight thumb indicates the direction).For an orientable surface S composed of a set of flat facet areas, the vector area of the surface is given bywhere is the unit normal vector to the area .For bounded, oriented curved surfaces that are sufficiently well-behaved, we can still define vector area. First, we split the surface into infinitesimal elements, each of which is effectively flat. For each infinitesimal element of area, we have an area vector, also infinitesimal.where is the local unit vector perpendicular to . Integrating gives the vector area for the surface.For a curved or faceted surface, the vector area is smaller in magnitude than the area. As an extreme example, a closed surface can possess arbitrarily large area, but its vector area is necessarily zero. Surfaces that share a boundary may have very different areas, but they must have the same vector area—the vector area is entirely determined by the boundary. These are consequences of Stokes theorem.The concept of an area vector simplifies the equation for determining the flux through the surface. Consider a planar surface in a uniform field. The flux can be written as the dot product of the field and area vector. This is much simpler than multiplying the field strength by the surface area and the cosine of the angle between the field and the surface normal.".
- Vector_area wikiPageID "3103326".
- Vector_area wikiPageRevisionID "580414312".
- Vector_area hasPhotoCollection Vector_area.
- Vector_area subject Category:Analytic_geometry.
- Vector_area subject Category:Area.
- Vector_area subject Category:Vectors.
- Vector_area type Abstraction100002137.
- Vector_area type Cognition100023271.
- Vector_area type Concept105835747.
- Vector_area type Content105809192.
- Vector_area type Idea105833840.
- Vector_area type PsychologicalFeature100023100.
- Vector_area type Quantity105855125.
- Vector_area type Variable105857459.
- Vector_area type Vector105864577.
- Vector_area type Vectors.
- Vector_area comment "In geometry, for a finite planar surface of scalar area , the vector area is defined as a vector whose magnitude is and whose direction is perpendicular to the plane, as determined by the right hand rule on the rim (moving one's right hand counterclockwise around the rim, when the palm of the hand is "touching" the surface, and the straight thumb indicates the direction).For an orientable surface S composed of a set of flat facet areas, the vector area of the surface is given bywhere is the unit normal vector to the area .For bounded, oriented curved surfaces that are sufficiently well-behaved, we can still define vector area. ".
- Vector_area label "Vector area".
- Vector_area label "Vettore area".
- Vector_area label "Wektor powierzchni".
- Vector_area sameAs Vettore_area.
- Vector_area sameAs Wektor_powierzchni.
- Vector_area sameAs m.08rm7n.
- Vector_area sameAs Q2615625.
- Vector_area sameAs Q2615625.
- Vector_area sameAs Vector_area.
- Vector_area wasDerivedFrom Vector_area?oldid=580414312.
- Vector_area isPrimaryTopicOf Vector_area.