Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇ f . 15. F ( x , y , z ) = 2 x y 3 z 2 , 3 x 2 y 2 z 2 , 2 x 2 y 3 z
Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇ f . 15. F ( x , y , z ) = 2 x y 3 z 2 , 3 x 2 y 2 z 2 , 2 x 2 y 3 z
Solution Summary: The author explains that a conservative vector field is one for which value of curl F is equal to zero.
Determine whether or not the vector field is conservative. If it is conservative, find a function
f
such that
F
=
∇
f
.
15.
F
(
x
,
y
,
z
)
=
2
x
y
3
z
2
,
3
x
2
y
2
z
2
,
2
x
2
y
3
z
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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