For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 348. Use Stokes’ theorem for vector field F ( x , y , z ) = − 3 2 y 2 i − 2 x y j + y z k , where S is that part of the surface of plane x + y + z = 1 contained within triangle C with vertices ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , and ( 0 , 0 , 1 ) , traversed counterclockwise as viewed from above.
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 348. Use Stokes’ theorem for vector field F ( x , y , z ) = − 3 2 y 2 i − 2 x y j + y z k , where S is that part of the surface of plane x + y + z = 1 contained within triangle C with vertices ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , and ( 0 , 0 , 1 ) , traversed counterclockwise as viewed from above.
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
348. Use Stokes’ theorem for vector field
F
(
x
,
y
,
z
)
=
−
3
2
y
2
i
−
2
x
y
j
+
y
z
k
, where S is that part of the surface of plane
x
+
y
+
z
=
1
contained within triangle C with vertices
(
1
,
0
,
0
)
,
(
0
,
1
,
0
)
, and
(
0
,
0
,
1
)
, traversed counterclockwise as viewed from above.
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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