Make a circle with O as the center and 1/√3 as the radius. Take a point A on the circle, connect OA, and take the midpoint P of OA. In P, the intersection with P is BC⊥OA, and in B and C, it is easy to get BC= 1.

Let q be the moving point on the lower arc BC, which is different from B and C, and it is easy to get: ∠BQC=2π/3.

Then: vector BC=β, vector QC=α, so: vector QB=α-β.

It is easy to verify that α and β are vectors that satisfy the conditions.

So: 0