A vector \( \vec{v} \) in the first octant is inclined to the x-axis at \( 60^\circ \), to the y-axis at \( 45^\circ \) and to the z-axis at an acute angle. If a plane passing through the points \( (\sqrt{2},-1,1) \) and \( (a,b,c) \), is normal to \( \vec{v} \), then:
