For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 355. Use Stokes’ theorem to compute ∬ s c u r l F ⋅ d S , where F ( x , y , z ) = i + x y 2 j + x y 2 k and S is a part of plane y + z = 2 inside cylinder x 2 + y 2 = 1 and oriented counterclockwise.
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 355. Use Stokes’ theorem to compute ∬ s c u r l F ⋅ d S , where F ( x , y , z ) = i + x y 2 j + x y 2 k and S is a part of plane y + z = 2 inside cylinder x 2 + y 2 = 1 and oriented counterclockwise.
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
355. Use Stokes’ theorem to compute
∬
s
c
u
r
l
F
⋅
d
S
, where
F
(
x
,
y
,
z
)
=
i
+
x
y
2
j
+
x
y
2
k
and S is a part of plane
y
+
z
=
2
inside cylinder
x
2
+
y
2
=
1
and oriented counterclockwise.
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.
Mathematics for Elementary Teachers with Activities (5th Edition)
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