Question
In: Advanced Math
Let F be a vector field. Find the flux of F through the given surface. Assume...
Let F be a vector field. Find the flux of F through the given
surface. Assume the surface S is oriented upward. F = eyi + exj +
24yk; S that portion of the plane x + y + z = 6 in the first
octant.
Solutions
Expert Solution
Since there is a confusing in reading vector field F,
Here, I assumed that 
. The solution is :-
Colby Messinger answered 2 years agoRelated Solutions
Compute the flux of the vector field F = <xy, 5yz, 6zx> through the portion of...
Compute the flux of the vector field F = <xy, 5yz, 6zx>
through the portion of the plane 3x + 2y + z = 6 in the first
octant with the downward orientation.
Find the flux of the vector field F = x i + e2x j + z ...
Find the flux of the vector field F =
x i +
e2x j +
z k through the surface S given
by that portion of the plane 2x + y +
8z = 7 in the first octant, oriented upward.
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = xy i + yz j + zx k
S is the part of the paraboloid
z = 6 − x2 − y2 that lies above the square
0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
and has...
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i − z j + y k
S is the part of the sphere
x2 + y2 + z2 = 1
in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i − z j + y k
S is the part of the sphere
x2 + y2 + z2 = 9
in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral
S
F ·
dS for the given
vector field F and the oriented surface
S. In other words, find the flux of F
across S. For closed surfaces, use the positive (outward)
orientation.
F(x, y, z) =
xzey i −
xzey j + z
k
S is the part of the plane x + y +
z = 3 in the first octant and has downward orientation
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i + y j + z4 k
S is the part of the cone z =
x2 + y2
beneath the plane
z = 1
with downward orientation
Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z...
Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z +
z^3 ) across the outward oriented faces of a cube without the front
face at x = 2 and with vertices at (0,0,0), (2,0,0), (0,2,0) and
(0,0,2).
Calculate the flux of the vector field F? (r? )=9r? , where r? =?x,y,z?, through a...
Calculate the flux of the vector field F? (r? )=9r? , where r?
=?x,y,z?, through a sphere of radius 4 centered at the origin,
oriented outward.
Flux =
(3) Let V be a vector space over a field F. Suppose that a ? F,...
(3) Let V be a vector space over a field F. Suppose that a ? F,
v ? V and av = 0. Prove that a = 0 or v = 0.
(4) Prove that for any field F, F is a vector space over F.
(5) Prove that the set V = {a0 + a1x + a2x 2 + a3x 3 | a0, a1,
a2, a3 ? R} of polynomials of degree ? 3 is a vector space over...
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