the larger of the two angles made with the x axis of a straight line drawn through [1,2]so that it intersect x+y=4 at a distance root6/3from [1,2] is

Dear jauneet singh

here distance form of a line is very helpful

equation of line

(x-1)/   =(y-2)/sinΘ  =√6 /3

 

so  x=1+√6 cosΘ  /3

 

and y =2 +√6 sinΘ /3

These point lie on the line x+y =4

 

so  1+√6 cosΘ  /3   +2 +√6 sinΘ /3 =4

 

or    √6 /3 (cosΘ +sinΘ) =1

or   1/√2 (cosΘ +sinΘ)  =√3 /2

 or        sin(Θ+45) =sin 60   or sin 120

 for  larger angle

   sin(Θ+45) =sin 120

    Θ=75

 

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