a) Determine whether or not the given vector field is conservative. b) Determine the interpretation of the result c) Verify that the solution of the problem satisfies all the conditions of Theorem 1. F(x, y, z) = xy²z³i + 2x²yz³j+3x²y ² z ² k Theorem 1 If F(x,y,z) is a field defined on all R3 whose component functions have continuous partial derivatives and rot F=0 then F(x,y,z) is a conservative vector field jk rot F= VxF= dx dy dz Q R rot F(x, y, z)= - (352) + (32-02)1 + (8-37)*
a) Determine whether or not the given vector field is conservative. b) Determine the interpretation of the result c) Verify that the solution of the problem satisfies all the conditions of Theorem 1. F(x, y, z) = xy²z³i + 2x²yz³j+3x²y ² z ² k Theorem 1 If F(x,y,z) is a field defined on all R3 whose component functions have continuous partial derivatives and rot F=0 then F(x,y,z) is a conservative vector field jk rot F= VxF= dx dy dz Q R rot F(x, y, z)= - (352) + (32-02)1 + (8-37)*
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:a) Determine whether or not the given vector field is conservative.
b) Determine the interpretation of the result
c) Verify that the solution of the problem satisfies all the conditions of Theorem 1.
F(x, y, z) = xy²z³i+2x²yz³j+3x²y²z²k
Theorem 1 If F(x,y,z) is a field defined on all R3 whose component functions have continuous partial derivatives and rot F=0 then F(x,y,z) is a conservative vector field
i
rot F = VXF=
Р
rot F(x, y, z) = (332) + (32-33) + (-35),
k
【JP
d
kaR
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