JEE Main · 2010 · 11 Apr 2010 · Offline · Three Dimensional Geometry

The midpoint of $A(3,1,6)$ and $B(1,3,4)$ is $(2,2,5)$, and substituting into $x-y+z$ gives $2-2+5=5$, so the midpoint lies on the plane and Statement-2 is true. The direction of $AB$ is $(2,-2,2)$, proportional to $(1,-1,1)$, which is the plane's normal, so $AB$ is perpendicular to the plane; together with the midpoint lying on it, $A$ is indeed the mirror image of $B$, so Statement-1 is true. But merely bisecting the segment is not enough to make a point a mirror image, the perpendicularity is also needed, so Statement-2 on its own does not fully explain Statement-1.