Divergence of radial fields Calculate the divergence of the following radial fields. Express the result in terms of the position vector r and its length | r |. Check for agreement with Theorem 17.10 20. F = 〈 x , y , z 〉 ( x 2 + y 2 + z 2 ) = r | r | 2
Divergence of radial fields Calculate the divergence of the following radial fields. Express the result in terms of the position vector r and its length | r |. Check for agreement with Theorem 17.10 20. F = 〈 x , y , z 〉 ( x 2 + y 2 + z 2 ) = r | r | 2
Solution Summary: The author analyzes the divergence of the radial vector field with the use of Theorem 17.10.
Divergence of radial fields Calculate the divergence of the following radial fields. Express the result in terms of the position vectorr and its length |r|. Check for agreement with Theorem 17.10
20.
F
=
〈
x
,
y
,
z
〉
(
x
2
+
y
2
+
z
2
)
=
r
|
r
|
2
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.
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by
= (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y-
direction.
(Use symbolic notation and fractions where needed.)
V. dS =
Image is attached.plz solve
A net is dipped in a river. Determine the
flow rate of water across the net if the
velocity vector field for the river is given
by v=(x-y,z+y+7,z2) and the net is
decribed by the equation y=1-x2-z2, y20,
and oriented in the positive y- direction.
(Use symbolic notation and fractions
where needed.)
University Calculus: Early Transcendentals (4th Edition)
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