A line l passing through the origin is perpendicular to the lines l1:(3+t)i^+(−1+2t)j^+(4+2t)k^, −∞

The given lines are l1:x−31=y+12=z−42=t, l2:x−32=y−32=z−21=sLet direction ratios of l be a,b,c then as l⊥l1 and l2∴a+2b+2c=02a+2b+c=0⇒a−2=b3=c−2∴l:x2=y−3=z2=λAny point on l1 is (t+3,2t−1,2t+4) and any point on l is (2λ,−3λ,2λ)∴ For Intersection point P of l and l1t+3=2λ,2t−1=−3λ,2t+4=2λ⇒t=−1,λ=1∴P(2,−3,2)Any point Q on l2 is (2s+3,2s+3,s+2)As per question PQ=17⇒(2s+1)2+(2s+6)2+s2=17⇒9s2+28s+20=0⇒s=−2,−109∴Point Q can be (-1,-1,0) and 79,79,89