Find the flux of the vector field F across σ in the direction of positive orientation. F( x , y , z ) = x i + y j + k; σ is the portion of the paraboloid r ( u , v ) = u cos v i + u sin v j+ ( 1 − u 2 ) k with 1 ≤ u ≤ 2 , 0 ≤ v ≤ 2 π .
Find the flux of the vector field F across σ in the direction of positive orientation. F( x , y , z ) = x i + y j + k; σ is the portion of the paraboloid r ( u , v ) = u cos v i + u sin v j+ ( 1 − u 2 ) k with 1 ≤ u ≤ 2 , 0 ≤ v ≤ 2 π .
Find the flux of the vector field F across
σ
in the direction of positive orientation.
F(
x
,
y
,
z
)
=
x
i
+
y
j
+
k;
σ
is the portion of the paraboloid
r
(
u
,
v
)
=
u
cos
v
i
+
u
sin
v
j+
(
1
−
u
2
)
k
with
1
≤
u
≤
2
,
0
≤
v
≤
2
π
.
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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