Let `A=hatiA cos theta+hatj A sin theta` be any vector .Another vector B which is perpendiculaar to A can be expressed as

Options

A. `B cos thetahat(i)-Bsin theta hat(j)`
B. `B sin theta hat(i)-B cos theta hat(j)`
C. `B cos theta hat(i)+Bsin theta hat(j)`
D. `B sin theta hat(i)+Bcos theta hat(j)`

Answer

B

Explanation

Clearly, `vec(B)` should be either in the second quadrant or the fourth quadrant. In none of the given options, we have `-hat(i)` term. So the second quadrant is ruled out. Also `vec(B)` should make an angle of `90^(@)- theta` with the x-axis (figure). So , B should be `vec(B) cos (90^(@)-theta) hat(i)-B sin (90^(@))hat(j)=Bsin theta hat(i)-B cos theta hat(j)`.
(##BMS_V01_C03_E01_078_S01.png" width="80%">