Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

A plane through the line: $3x-y+2z-1+\lambda (x+2y-z-2)=0$. It is perpendicular to $3x+2y+z=0:3(3+\lambda )+2(2\lambda -1)+(2-\lambda )=0$, so $9+6\lambda =0,\lambda =-\frac{3}{2}$. The plane is $3x-8y+7z+4=0$, so the projection is $3x-8y+7z+4=0=3x+2y+z$ (B). Its direction ratios are $(3,-8,7)\times (3,2,1)\propto (11,-9,-15)$ and $(-1,1,1)$ lies on both planes, giving A. In C the direction is (11, -9, 15) and in D the point (-12, -8, -14) is not on $3x+2y+z=0$.