The correct option is D ^iBsinθ−^jBcosθ
→A.→B must be zero, which is the case for option C only. Dot products of different options are given as:
A. ABcos2θ−ABsin2θ, not zero.
B. ABcos2θ+ABsin2θ=AB, not zero.
C. ABcosθsinθ−ABsinθcosθ=0
D. ABcosθsinθ+ABsinθcosθ, not zero