Vectors which is perpendicular to `( a cos theta hat (i) + b sin theta hat(j))` is

Options

A. `b sintheta hati-a costheta hatj`
B. `(1)/(a)sin theta hati -(1)/(b) cos theta hat j`
C. `5 hat k `
D. All of these

Answer

A

Explanation

If two vectors are pendicular to each other, then their dot product must be equal to zero.
i.e., `x*y=0`
Given, `x=a cos theta hati +b sin theta hatj`
Now, if `y=b sin theta hati - a cos theta hat j `
then
`x*y=(a cos theta hati + b sin theta hat j)*(b sin theta hati - a cos theta hat j)`
`xy=ab sin theta cos theta - ab sin theta cos theta =0`
Hence, vectors are perpendicular
when `y=b sin theta hati -a cos hatj`
Similarly, for options (b) and (c )
also xy = 0.