Let \( \triangle ABC \) be the triangle such that the equations of lines \( AB \) and \( AC \) be \( 3y - x = 2 \) and \( x + y = 2 \), respectively, and the points \( B \) and \( C \) lie on \( x \)-axis. If \( P \) is the orthocentre of the triangle \( ABC \), then the area of the triangle \( PBC \) is equal to:
