Vector which is perpendicular to (acosθ)i^+(bsinθ)j^  is given by :

(i)[(acosθ)i^+(bsinθ)j^].[(bsinθ)i^−(acosθ)j^] =absinθcosθ−basinθcosθ=0 (ii)[a(cosθ)i^+(bsinθ)j^].[(1asinθ)i^−(1bcosθ)j^]=sinθcosθ−sinθcosθ=0(iii)[(acosθ)i^+(bsinθ)j^].5k^=0Hence, all the three options are correct because the dot product of two perpendicular vectors is zero