For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D . 405. Evaluate ∬ s F ⋅ N d s , where F ( x , y , z ) = x 2 i + x y j + x 3 y 3 k and S is the surface consisting of all faces except the tetrahedron bounded by plane x + y + z = 1 and the coordinate planes, with outward unit normal vector N .
For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D . 405. Evaluate ∬ s F ⋅ N d s , where F ( x , y , z ) = x 2 i + x y j + x 3 y 3 k and S is the surface consisting of all faces except the tetrahedron bounded by plane x + y + z = 1 and the coordinate planes, with outward unit normal vector N .
For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D.
405. Evaluate
∬
s
F
⋅
N
d
s
, where
F
(
x
,
y
,
z
)
=
x
2
i
+
x
y
j
+
x
3
y
3
k
and S is the surface consisting of all faces except the tetrahedron bounded by plane
x
+
y
+
z
=
1
and the coordinate planes, with outward unit normal vector N.
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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