If α→+β→+γ→=kδ→ and β→+γ→+δ→=mα→,α→ and δ→ are non-collinear, then α→+β→+γ→+δ→ equal
kα→
mδ→
0→
(k+m)γ→
Given α→+β→+γ→=kδ→----i
β→+γ→+δ→=mα→----ii
From(i), α→+β→+γ→+δ→=(k+1)δ→---iii
From (ii), α→+β→+γ→+δ→=(m+1)α→----iv
From (iii) and (iv), we get
(k+1)δ→=(m+1)α→-----v
Since α→ is not parallel to δ→,
From (v),k+1=0and m+ 1=0
From (iii), α→+β→+γ→+δ→=0→