Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The midpoint of the line segment joining $P(1,2,5)$ and $Q(3,4,3)$ is given by $\left(\frac{1+3}{2},\frac{2+4}{2},\frac{5+3}{2}\right)=(2,3,4)$.

The normal vector to the plane is parallel to the vector $\overrightarrow{PQ}$.

Direction ratios of $\overrightarrow{PQ}$ are $(3-1,4-2,3-5)=(2,2,-2)$.

Taking the direction ratios of the normal to the plane as $(1,1,-1)$.

The equation of the plane passing through $(2,3,4)$ with normal direction ratios $(1,1,-1)$ is

$1(x-2)+1(y-3)-1(z-4)=0$

$x+y-z-2-3+4=0$

$x+y-z-1=0$

Answer: $x+y-z-1=0$