JEE Main 2022 (Online) 27th June Morning ShiftQuestion 1
If two straight lines whose direction cosines are given by the relations $l+m-n=0$, $3l^{2}+m^{2}+cnl=0$ are parallel, then the positive value of $c$ is :
3D Geometry
Solution
Substituting $n=l+m$ the second relation is $3l^2+m^2+c\,l(l+m)=0$, i.e. $(3+c)l^2+c\,lm+m^2=0$. Parallel lines means equal roots in $l/m$: $c^2-4(3+c)=0\Rightarrow c^2-4c-12=0\Rightarrow c=6$ or $-2$. Positive value $6$. Option (A).