On restricted projections to planes in ℝ3

Let γ:[0,1]² be a non-degenerate curve in R³, that is to say, (γ(θ),γ'(θ),γ" (θ))≠ 0. For each θ∈[0,1], let V_θ=γ(θ)^⊥ and let π_θ:R³→ V_θ be the orthogonal projections. We prove that if A³ is a Borel set, then for a.e. θ∈ [0,1] we have (π_θ(A))=min\2, A\. More generally, we prove an exceptional set estimate. For A³ and 0≤ s≤ 2, define Eₛ(A):=\θ∈[0,1]:(π_θ(A))<s\. We have (Eₛ(A))≤max\1+s-(A),0\. We also prove that if (A)>2, then for a.e. θ∈[0,1] we have H²(π_θ(A))>0.