If the dr’s of two lines are given by 3lm−4ln+mn=0 and l+2m+3n=0 then the angle between the lines is

l+2m+3n=0⇒l=−2m−3n3lm−4ln+nm=0⇒3m(−2m−3n)−4n(−2m−3n)+mn=0  ⇒−6m2−9mn+8mn+12n2+mn=0⇒12n2=6m2⇒m=±2n,l=(+22)nD.r’s of the lines are  (−22−3,2,1)(22−3,−2,1)∴a1a2+b1b2+c1c2=(−22−3)(22−3)−2+1=9−8−2+1=0⇒ Required angle =π2