Which of the following vectors is perpendicular to Pcosθ i +Qsinθ j?

Question : Which of the following vectors is perpendicular to Pcosθ i +Qsinθ j?

a) Psinθ i + Qcosθ j

b) Qsinθ i - Pcosθ j

c) Pcosθ i + Qsinθ j

d) Qcosθ i - Psinθ j

Doubt by Niyati

Solution : 
We know, Scalar (Dot) Product of two vectors is always equals to zero. 

Let A = Pcosθ i +Qsinθ j 

a) B = Qsinθ i + Pcosθ j

A.B = P²sinθcosθ + Q²sinθcosθ

A.B ≠ 0

b) B = Qsinθ i - Pcosθ j

A.B = PQsinθcosθ - PQsinθcosθ

A.B = 0

c) B = Pcosθ i + Qsinθ j

A.B = P²cos²θ + Q²sin²θ

A.B ≠ 0

d) B = Qcosθ i - Psinθ j

A.B = PQcos²θ - PQsin²θ

A.B ≠ 0

Hence, b) is the correct answer.