For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 353. Use Stokes’ theorem to evaluate ∮ F ⋅ d S , where F ( x , y , z ) = y i + z j + x k and C is a triangle with vertices ( 0 , 0 , 0 ) , ( 2 , 0 , 0 ) and ( 0 , − 2 , 0 ) oriented counterclockwise when 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. 353. Use Stokes’ theorem to evaluate ∮ F ⋅ d S , where F ( x , y , z ) = y i + z j + x k and C is a triangle with vertices ( 0 , 0 , 0 ) , ( 2 , 0 , 0 ) and ( 0 , − 2 , 0 ) oriented counterclockwise when 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.
353. Use Stokes’ theorem to evaluate
∮
F
⋅
d
S
, where
F
(
x
,
y
,
z
)
=
y
i
+
z
j
+
x
k
and C is a triangle with vertices
(
0
,
0
,
0
)
,
(
2
,
0
,
0
)
and
(
0
,
−
2
,
0
)
oriented counterclockwise when 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.
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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