Verify Formula (2) in stokes’ Theorem by evaluating the line integral and the surface integral. Assume that the surface has an upward orientation. F ( x , y , z ) = ( z − y ) i+( z + x ) j − ( x + y ) k; σ is the portion of the parabolid z = 9 − x 2 − y 2 above the x y -plane .
Verify Formula (2) in stokes’ Theorem by evaluating the line integral and the surface integral. Assume that the surface has an upward orientation. F ( x , y , z ) = ( z − y ) i+( z + x ) j − ( x + y ) k; σ is the portion of the parabolid z = 9 − x 2 − y 2 above the x y -plane .
Verify Formula (2) in stokes’ Theorem by evaluating the line integral and the surface integral. Assume that the surface has an upward orientation.
F
(
x
,
y
,
z
)
=
(
z
−
y
)
i+(
z
+
x
)
j
−
(
x
+
y
)
k;
σ
is the portion of the parabolid
z
=
9
−
x
2
−
y
2
above
the
x
y
-plane
.
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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