For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 338. [T] Use a CAS and Stokes’ theorem to approximate line integral ∫ c [ ( 1 + y ) z d x + ( 1 + z ) x d y + ( 1 + x ) y d z ] , where C is a triangle with vertices ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , and ( 0 , 0 , 1 ) 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. 338. [T] Use a CAS and Stokes’ theorem to approximate line integral ∫ c [ ( 1 + y ) z d x + ( 1 + z ) x d y + ( 1 + x ) y d z ] , where C is a triangle with vertices ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , and ( 0 , 0 , 1 ) 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.
338. [T] Use a CAS and Stokes’ theorem to approximate line integral
∫
c
[
(
1
+
y
)
z
d
x
+
(
1
+
z
)
x
d
y
+
(
1
+
x
)
y
d
z
]
, where C is a triangle with vertices
(
1
,
0
,
0
)
,
(
0
,
1
,
0
)
, and
(
0
,
0
,
1
)
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.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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