# Conservative Vector Field??

Discussion in 'Undergraduate Math' started by SGod88, Nov 10, 2007.

1. ### SGod88Guest

I am encountering a problem in line integral.. I dont know how to
relate this to a conservative vector field.. It is good that some
hints will be given to solve this question..

Consider a closed polygon with vertices,v_1,v_2,...,v_n,v_(n+1)=v_1,
arranged in the positive direction (anticlockwise) and let v be a
point inside the polygon.

Show that
sum( w_j*v_j, j=2..n)
v= --------------------------------------
sum( w_j, j=2..n)

where
tan[ (alpha_(j-1)/2 ] + tan [ alpha(j)/2 ]
wj= ------------------------------------------------------------
||vj-
v||
j=2,3,...n +1

and

alpha_ j is the angle at v with |alpha(j)|<PI, of the oriented
triangle [v,vj,vj+1] taking positive value if the orientation is
positive and negative value otherwise.

I am not clear how this problem lead to the concept of line integral
and conservtive vector field...

So far I found that it only can be written as

v_j
sum(w_j*v_j)= ------------------------- * {(tan[ (alpha_(j-1)/2 ] +
tan [ alpha(j)/2 ] }
||vj-v||

and v=(x,y,z), v_j=(x_j,y_j,z_j)..

then how should I continue this? Any hints? Thanks a lot!

SGod88, Nov 10, 2007