- #1
mathwizeguy
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Are area vectors of oriented surfaces always perpendicular to the surface?
In summary, area vectors of oriented surfaces refer to the direction and magnitude of the area of a surface. They are calculated by taking the cross product of two tangent vectors on the surface and are used to determine the orientation of the surface. Area vectors are significant in scientific fields such as physics and engineering, as they are used to calculate flux and determine the direction of a force on a surface. They are related but not the same as surface area, as they provide additional information about the orientation of the surface. Area vectors can be negative, indicating an opposite orientation, but the magnitude still represents the area of the surface.
- #2
tiny-tim
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welcome to pf!
ih mathwizeguy! welcome to pf!
simple answer … yes!
ih mathwizeguy! welcome to pf!
mathwizeguy said:
simple answer … yes!
- #3
lugita15
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Also, you should know that the convention is for the area vector to point out of the surface.
- #4
HallsofIvy
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Such a convention would only hold for a closed surface. You can, more generally, refer to "upward" or "downward" normals, "inward" or "outward" normals, etc.lugita15 said:
Related to Area vectors of oriented surfaces
What are area vectors of oriented surfaces?
Area vectors of oriented surfaces refer to the direction and magnitude of the area of a surface. They are used to determine the orientation of a surface and are represented by a vector perpendicular to the surface.
How are area vectors of oriented surfaces calculated?
Area vectors of oriented surfaces are calculated by taking the cross product of two tangent vectors on the surface. The resulting vector will be perpendicular to the surface and its direction will indicate the orientation of the surface.
What is the significance of area vectors in science?
Area vectors are important in many scientific fields such as physics and engineering. They are used to calculate the flux of a vector field through a surface and are also useful in determining the direction of a force acting on a surface.
What is the difference between area vectors and surface area?
Area vectors and surface area are related but not the same. Area vectors indicate the direction and magnitude of the area of a surface, while surface area refers to the actual measurement of the surface's area. Area vectors are used to calculate surface area, but they also provide additional information about the orientation of the surface.
Can area vectors be negative?
Yes, area vectors can be negative. This indicates that the surface is oriented in the opposite direction of the vector. However, the magnitude of the vector will still represent the area of the surface, regardless of its direction.
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