Math 213 Homework 6 Spring 2014  
1. Find the line integral of vector field F  r  
y , x, z over a path connecting points (0,0,1) and (1,0,1) and consisting of a parabolic segment C1 and a straight line C2, as indicated in the figure z 1
C1
P(1,0,1)
z =1y2
C2
1
x
y
1
 
2. Consider the vector field F  r   x  y, x : a) Sketch this vector field in the x‐y plane b) Find the total circulation of this vector field around a triangular closed curve connecting vertices (0,0), (2,0) and (0,1). c) Find the flux of this vector field across a circle of radius 2 centered at the origin  
 
2
xz
xz
2
xz
. 3. Consider vector field F  r   z  y z e , e  2 y sin y , 2 xz  xye
 

 
a. Show that F  r  is conservative by calculating its curl ,   F  r  b. Find the potential function of this vector field. c. Find total work performed by this force over a path from point (1, 0, 0) to point (0,  , 1) 

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