Given that equation of lines are 2x−3y=4 ...(i) and x+y=1 or x+y−1=0 ...(ii) Now, let any line parallel to x+y−1=0 is given by x+y+λ=0 which passes through (1, 1). ∴1+1+λ=0⇒λ=−2 ∴ Required line is x+y−2=0 or x+y=2 ...(iii) ∴ Point of intersection of lines (i) and (iii) is (2,0) ∴ Required distance =√(2−1)2+(0−1)2=√1+1=√2