Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Since the plane bisects seg $AB$, the plane meets the line $AB$ at the mid point i.e. $\left(\frac{3+1}{2},\frac{2+4}{2},\frac{-1+3}{2}\right)\equiv (2,3,1)$ Now line $AB$ is $\perp$ er to the plane Direction ratios of plane are $1-3,4-2,3+1$ i.e. $-2,2,4$ i.e. $-1,1,2$ Equation of plane passing through $(2,3,1)$ and having d.r.s. $(-1,1,2)$ are $-(x-2)+(y-3)+2(z-1)=0\Rightarrow -x+2+y-3+2z-2=0$ $\therefore x-y-2z+3=0$