For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 347. Use Stokes’ theorem for vector field F ( x , y , z ) = z i + 3 x j + 2 z k where S is surface z = 1 − x 2 − 2 y 2 , z ≥ 0 , C is boundary circle x 2 + y 2 = 1 , and S is oriented in the positive z -direction.
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 347. Use Stokes’ theorem for vector field F ( x , y , z ) = z i + 3 x j + 2 z k where S is surface z = 1 − x 2 − 2 y 2 , z ≥ 0 , C is boundary circle x 2 + y 2 = 1 , and S is oriented in the positive z -direction.
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
347. Use Stokes’ theorem for vector field
F
(
x
,
y
,
z
)
=
z
i
+
3
x
j
+
2
z
k
where S is surface
z
=
1
−
x
2
−
2
y
2
,
z
≥
0
, C is boundary circle
x
2
+
y
2
=
1
, and S is oriented in the positive z-direction.
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)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.