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Given: vec(A)=Acos theta hat(i)+Asin the...

Given: `vec(A)=Acos theta hat(i)+Asin theta hat(j)`. A vector `vec(B)`, which is perpendicular to `vec(A)`,is given by

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)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`.
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