Step 1: Understanding the Concept:
The XY plane is the horizontal plane where the z-coordinate is zero everywhere. Any plane that is parallel to the XY plane will have a constant height, meaning its z-coordinate is constant for all points lying on it.
Step 2: Key Formula or Approach:
The general equation of a plane parallel to the XY plane is of the form $z = c$, where $c$ is a constant representing the perpendicular distance from the XY plane.
Step 3: Detailed Explanation:
We are given that the required plane is parallel to the XY plane.
Therefore, its equation must be of the form $z = c$.
We are also given that the plane passes through the point A$(7, 8, 6)$.
Since the point A lies on the plane, its coordinates must satisfy the plane's equation.
Substituting the coordinates of A$(7, 8, 6)$ into the equation $z = c$, we equate the z-coordinate of the point to $c$:
\[ 6 = c \]
Therefore, the constant $c$ is $6$.
Substituting this back, the exact equation of the plane is $z = 6$.
Step 4: Final Answer:
The required equation is $z = 6$.