What will be the equation of line for which p = 3 and D = 120° ?

Here,

p = 3 and α = 120°

x cos α + y sin α = p

⇒ x cos 120° + y sin 120° = 3

⇒ x cos (180° – 60°) + y sin (180° – 60°) = 3

⇒ –x cos 60° + y sin 60° = 3

cos (180° – θ) = –cosθ

sin (180° – θ) = sinθ

$\Rightarrow-\frac{x}{2}+y \frac{\sqrt{3}}{2}=3$

$\Rightarrow-x+\sqrt{3} y=6$