If `x cos theta + y sin theta =2` is perpendicular to the line x-y =3 then what is one of the value of `theta`?

Options

A. `pi//6`
B. `pi//4`
C. `pi//2`
D. `pi//3`

Answer

B

Explanation

consider a line
`x theta + y sin theta =2`
`rarr y =- x(cos theta)/(sin theta)+(2)/(sin theta)`
`rarr y=-x cot theta + 2 cosec theta`
On comparing this equaiton with
`y = mx + c` we get
slope of line x cos `theta +sin theta =2 is -cot theta`
Also we have a line x-y =3
`rarr y=x-3`
slope of line x -y =3 is 1
Since both the ines are perpendicualr to ech other
`therefore`Product of their slopes =-1
`rarr (-cot theta) (1)=-1`
`rarr theta = (pi)/(4)`