For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 356. Use Stokes’ theorem to evaluate ∬ s c u r l F ⋅ d S where F ( x , y , z ) = − y 2 i + x j + z 2 k and S is the part of plane x + y + z = 1 in the positive octant and oriented counterclockwise x ≥ 0 , y ≥ 0 , z ≥ 0 .
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 356. Use Stokes’ theorem to evaluate ∬ s c u r l F ⋅ d S where F ( x , y , z ) = − y 2 i + x j + z 2 k and S is the part of plane x + y + z = 1 in the positive octant and oriented counterclockwise x ≥ 0 , y ≥ 0 , z ≥ 0 .
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
356. Use Stokes’ theorem to evaluate
∬
s
c
u
r
l
F
⋅
d
S
where
F
(
x
,
y
,
z
)
=
−
y
2
i
+
x
j
+
z
2
k
and S is the part of plane
x
+
y
+
z
=
1
in the positive octant and oriented counterclockwise
x
≥
0
,
y
≥
0
,
z
≥
0
.
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.
Probability And Statistical Inference (10th Edition)
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