Given: A→=Acos⁡θi^+Asin⁡θj^. A vector B→, which is perpendicular to A→, is given by

Clearly, B→ should be either in the second quadrant or the fourth quadrant. In none of the given options, we have-i^ term. So the second quadrant is ruled out. Also B→should make an angle of 90o - θ with the x-axis (figure). So, B should be B→ cos (90o - θ) i^−Bsin⁡90∘−θj^=Bsin⁡θi^−Bcos⁡θj^