JEE Main 2021 (Online) 27th August Morning ShiftQuestion 1
Equation of a plane at a distance $\sqrt{\frac{2}{21}}$ from the origin, which contains the line of intersection of the planes $x-y-z-1=0$ and $2x+y-3z+4=0$, is :
3D Geometry
Solution
Plane $(1+2\lambda)x+(\lambda-1)y-(1+3\lambda)z+(4\lambda-1)=0$; distance$^2=\frac{(4\lambda-1)^2}{14\lambda^2+8\lambda+3}=\frac2{21}$ gives $308\lambda^2-184\lambda+15=0$, $\lambda=\frac12$ (or $\frac{15}{154}$). $\lambda=\frac12$ gives $4x-y-5z+2=0$.