Prove that when the sides of a triagle are taken in order, it leads to zero resultant.

Explanation

Let ABC be a triangle such that
`vec(BC)=vec a,vec(CA)=vec b` and `vec(AB)=vec c`. Then,
`rArr veca+vecb+vecc=vec(BC)+vec(CA)+vec(AB)`
`rArr vec a+vec b+vec c=vec(BA)+vec(AB)" " {"Since" vec(BC)+vec(CA)=vec(BA)}`
`rArr vec a+vec b+vec c=vec(BB)" "` [By triangle law]
`rArr veca+vecb+vec c" "` [By def. of null vector]
Hence `rArr veca+vecb+vec c=0`
`rArr vec(AB) +vec(BC)+vec(CA)=vec0`
`:.` When the sides of triangle are taken in order it leads to zero resultant.