Find the flux of the vector field F across σ . F( x , y , z ) = 5 z i + y j + 2 x k ; σ is the rectangle 0 ≤ x ≤ 2 , 0 ≤ y ≤ 3 in the plane z = 2 , oriented in the positive z- direction.
Find the flux of the vector field F across σ . F( x , y , z ) = 5 z i + y j + 2 x k ; σ is the rectangle 0 ≤ x ≤ 2 , 0 ≤ y ≤ 3 in the plane z = 2 , oriented in the positive z- direction.
F(
x
,
y
,
z
)
=
5
z
i
+
y
j
+
2
x
k
;
σ
is the rectangle
0
≤
x
≤
2
,
0
≤
y
≤
3
in the plane
z
=
2
,
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.
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