Prove that the sum of the vectors represented by the sides of a closed polygon taken in order is a zero vector.

Explanation

Then by triangle law
`vec(AB)+vec(BC) = vec(AC), vec(AC)+vec(CD) = vec(AD)`
`vec(AD)+vec(DE) = vec(AE), vec(EF)+vec(FA) = vec(EA)`
Adding the above relations we get
`vec(AB)+vec(BC)+vec(AC)+vec(CD)+vec(AD)+vec(DE)+vec(EF)+vec(FA) = vec(AC)+vec(AD)+vec(AE)+vec(EA)`
`implies vec(AB)+vec(BC)+vec(CD)+vec(DE)+vec(EF)+vec(FA)`
=`vec(AE)+vec(EA) = 0`