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If x cos theta + y sin theta =2 is perpe...

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`?

A

`pi//6`

B

`pi//4`

C

`pi//2`

D

`pi//3`

Text Solution

Verified by Experts

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)`
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