Let F( x , y , z ) = 6 a + 1 x i − 4 a y j+ a 2 z k and let σ be the sphere of a radius a centered at the origin and oriented outward. Use a CAS to find all values of a such that flux of F across σ is zero.
Let F( x , y , z ) = 6 a + 1 x i − 4 a y j+ a 2 z k and let σ be the sphere of a radius a centered at the origin and oriented outward. Use a CAS to find all values of a such that flux of F across σ is zero.
Let
F(
x
,
y
,
z
)
=
6
a
+
1
x
i
−
4
a
y
j+
a
2
z
k
and let
σ
be the sphere of a radius a centered at the origin and oriented outward. Use a CAS to find all values of a such that flux of F across
σ
is zero.
Find the flux of F=z2kF=z2k upward through the part of the sphere x2+y2+z2=a2x2+y2+z2=a2 in the first octant of 3-space.
The vector v = <a, 1, -1>, is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).
Find a.
Suppose is a constant vector. Let F(x, y, z) = C find the flux of F through a surface
S on plane with nonzero vectors A, B. In particular, the surface S is parametrized by
Flu, 0) = rõ tuổ+ vB for (u,v) er.
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