Find the flux of the vector field F across σ . F ( x , y , z ) = x 2 i + ( x + e y ) j − k; σ is the vertical rectangle 0 ≤ x ≤ 2 , 0 ≤ z ≤ 4 in the plane y = − 1 , oriented in the negative y- direction.
Find the flux of the vector field F across σ . F ( x , y , z ) = x 2 i + ( x + e y ) j − k; σ is the vertical rectangle 0 ≤ x ≤ 2 , 0 ≤ z ≤ 4 in the plane y = − 1 , oriented in the negative y- direction.
F
(
x
,
y
,
z
)
=
x
2
i
+
(
x
+
e
y
)
j
−
k;
σ
is the vertical rectangle
0
≤
x
≤
2
,
0
≤
z
≤
4
in the plane
y
=
−
1
,
oriented in the negative y-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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