1.
Let α⃗\vec{\alpha}, β⃗\vec{\beta}, γ⃗\vec{\gamma} be three unit vectors such that α⃗⋅β⃗=α⃗⋅γ⃗=0\vec{\alpha} \cdot \vec{\beta} = \vec{\alpha} \cdot \vec{\gamma} = 0 and the angle between β⃗\vec{\beta} and γ⃗\vec{\gamma} is 30∘30^{\circ}. Then α⃗\vec{\alpha} is