True or False? Justify your answer with a proof or a counterexample.
427. Vector field
F
(
x
,
y
)
=
x
2
y
i
+
y
2
x
j
is conservative.
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.
Expert Solution & Answer
To determine
To calculate:
To check whether the given statement is true or false.
Vector field F=x2yi+y2xj is conservative.
Answer to Problem 427RE
True.
Explanation of Solution
Given information:
Vector field F=x2yi+y2xj
Calculation:
Here the vector field is two dimensional of the form
F = Pi + Qj
F is said to be conservative if ∂P∂y=∂Q∂x:
Here ∂P∂y=2xy:∂Q∂x=2yx=2xy:
Since the condition required is satisfied F is conservative.
The given statement is true.
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