(a.b+bc+c.a) Use the relation, |a+b+c|2=[|a|2+|b|2+|c|2+2(a.b+b.c+ca)] We can write [λ2+λ2+λ2+2(a.b+b.c+c.a)]≥0 2(a.b+b.c+c.a)≥−3λ2 a.b+b.c+c.a>
−3λ2
2
Then cos‌α+cos‌β+cos‌γ≥
1
λ2
(
−3λ2
2
)=−
3
2
Therefore, the minimum value of the required equation is