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Chapter 14: Q. 37 (page 1096)

Show that the vector fields in Exercises 33鈥�40 are not conservative.

F(x,y,z)=2i-zj+eyzk

Short Answer

Expert verified

The vector fields is not conservative because 鈭�F1鈭�z鈮�鈭�F2鈭�y.

Step by step solution

01

Step 1. Given Information

We have to show that the vector fields in the given exercise is not conservative.
F(x,y)=2i-zj+eyzk

02

Step 2. A vector field F(x,y)=(F1(x,y),F2(x,y)) is not conservative if and only if ∂F1∂z≠∂F2∂y.

For the vector fieldF(x,y)=2i-zj+eyzk

鈭�F1鈭�z=鈭�鈭�z(-z)鈭�F1鈭�z=-1

03

Step 3. Now finding ∂F2∂y

鈭�F2鈭�y=鈭�鈭�yeyz鈭�F2鈭�y=zeyz

Hence, 鈭�F1鈭�z鈮�鈭�F2鈭�y.

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