If a(α→×β→)+b(β→×γ→)+c(γ→×α→)=0  and at least one of a, b and c is non-zero, then vectors α→,β→ and γ→ are

Taking dot Product of  a(α→×β→)+b(β→×γ→)+c(γ→×α→)=0 with α→,β→ and γ→ respectivelywe have,a[α→β→γ→]=0b[α→β→γ→]=0c[α→β→γ→]=0Since at least one of a, b and c ≠ 0, we have [α→β→γ→]=0Hence, α→,β→ and γ→ are co-planar.