Surface integrals of vector fields Find the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or parametric description of the surface . 47. F = r / | r | 3 across the sphere of radius a centered at the origin, where r = 〈 x , y , z 〉; normal vectors point outward.
Surface integrals of vector fields Find the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or parametric description of the surface . 47. F = r / | r | 3 across the sphere of radius a centered at the origin, where r = 〈 x , y , z 〉; normal vectors point outward.
Surface integrals of vector fieldsFind the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or parametric description of the surface.
47.
F
=
r
/
|
r
|
3
across the sphere of radius a centered at the origin, where r = 〈x, y, z〉; normal vectors point outward.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Fur
Find the area of the surface.
Syr
The helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v) i + u sin(v) j + v k, 0 s u s 1, 0 s vs 5x.
Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector VF(x, y, z).]
Point
(24, 10, 26)
Surface
z = √x² +₁
² + y²
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Find the area of the surface.
The helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v) i + u sin(v) j + v k, 0
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