Find the flux of the vector field F across σ . F ( x , y , z ) = x i + y j + 2 z k; σ is the portion of the surface z = 1 − x 2 − y 2 above the xy - plane, oriented by upward normals.
Find the flux of the vector field F across σ . F ( x , y , z ) = x i + y j + 2 z k; σ is the portion of the surface z = 1 − x 2 − y 2 above the xy - plane, oriented by upward normals.
F
(
x
,
y
,
z
)
=
x
i
+
y
j
+
2
z
k;
σ
is the portion of the surface
z
=
1
−
x
2
−
y
2
above the xy-plane, oriented by upward normals.
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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