Prove that the lines x=py+q,z=ry+s and x=p'y+q',z=r'y+s' are perpendicular, if pp'+n'+1=0.
We have, x=py+q⇒y=x−qP ...(i)
and z=ry+s⇒y=z−sr ...(ii)
⇒x−qp=y1=z−sr [using Eqs.(i) and (ii)] ...(iii)
Similarly, x−q′p′=y1=z−s′r′ ...(iv)
From Eqs. (iii) and (iv), a1=p,b−1=1,c1=r and a2=p′,b−2=1,c2=r′
If these given lines are perpendicular to each other, then
which is the required condition.