For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 357. Let F ( x , y , z ) = x y i + 2 z j − 2 y k and let C be the intersection of plane x + z = 5 and cylinder x 2 + y 2 = 9 , which is oriented counterclockwise when viewed from the top. Compute the line integral of F over C using Stokes’ theorem.
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 357. Let F ( x , y , z ) = x y i + 2 z j − 2 y k and let C be the intersection of plane x + z = 5 and cylinder x 2 + y 2 = 9 , which is oriented counterclockwise when viewed from the top. Compute the line integral of F over C using Stokes’ theorem.
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
357. Let
F
(
x
,
y
,
z
)
=
x
y
i
+
2
z
j
−
2
y
k
and let C be the intersection of plane
x
+
z
=
5
and cylinder
x
2
+
y
2
=
9
, which is oriented counterclockwise when viewed from the top. Compute the line integral of F over C using Stokes’ theorem.
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.
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