Statement-1: The point $$A(3, 1, 6)$$ is the mirror image of the point $$B(1, 3, 4)$$ in the plane $$x - y + z = 5$$. 

Statement-2: The plane $$x - y + z = 5$$ bisects the line segment joining $$A(3, 1, 6)$$ and $$B(1, 3, 4)$$.

1. Test Statement-2 (Bisection Condition)

For a plane to bisect the line segment joining two points, the midpoint of those two points must lie exactly on the plane.

Let us calculate the coordinates of the midpoint $$M$$ of line segment $$AB$$ using the midpoint formula:

$$M = \left(\frac{3 + 1}{2}, \frac{1 + 3}{2}, \frac{6 + 4}{2}\right) = (2, 2, 5)$$

Now substitute the coordinates of $$M(2, 2, 5)$$ into the equation of the plane $$x - y + z = 5$$:

$$2 - 2 + 5 = 5$$

$$5 = 5$$

Since the midpoint satisfies the plane equation, the plane bisects the segment $$AB$$. Thus, Statement-2 is True.

2. Test Statement-1 (Mirror Image Condition)

For point $$A$$ to be the exact mirror image of point $$B$$ in a plane, two conditions must be fulfilled:

The plane must bisect the segment $$AB$$ (Verified in step 1).

The line joining $$A$$ and $$B$$ must be perpendicular to the plane.

Let us find the direction ratios of the line segment $$\vec{AB}$$:

$$\vec{AB} = (1 - 3)\hat{i} + (3 - 1)\hat{j} + (4 - 6)\hat{k} = -2\hat{i} + 2\hat{j} - 2\hat{k}$$

Now, extract the normal vector $$\vec{n}$$ from the coefficients of the plane equation $$x - y + z = 5$$:

$$\vec{n} = 1\hat{i} - 1\hat{j} + 1\hat{k}$$

Check if the line vector $$\vec{AB}$$ is parallel to the normal vector $$\vec{n}$$:

$$\vec{AB} = -2(1\hat{i} - 1\hat{j} + 1\hat{k}) = -2\vec{n}$$

Since $$\vec{AB}$$ is a scalar multiple of $$\vec{n}$$, the line segment is perfectly perpendicular to the plane. Since both the bisection and perpendicularity conditions are satisfied, $$A$$ is the true mirror image of $$B$$. Thus, Statement-1 is True.

3. Evaluate the Explanation Relationship

Statement-2 only covers the bisection criteria. It does not mention or explain the perpendicularity requirement, which is essential to confirm a mirror image reflection. Therefore, Statement-2 is not the complete or correct explanation for Statement-1.

Final Answer
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.