Problem 7
Question
Find the intercepts and sketch the graph of the plane. $$ z=8 $$
Step-by-Step Solution
Verified Answer
The Z intercept of the plane \(z = 8\) is at z=8. The plane does not have X and Y intercepts since it is parallel to the X-Y plane. The graph of the plane reveals a line parallel to the x-y plane, passing through the point (0,0,8).
1Step 1: Define the plane equation
The equation of the plane is given by \(z = 8\). This plane is parallel to the x-y plane and intersects the z-axis at 8 units.
2Step 2: Find X and Y intercepts
The plane is parallel to X-Y plane, meaning it doesn't intersect the X and Y axes. Hence, there would be no X and Y intercepts.
3Step 3: Find Z intercept
The Z intercept is found where the plane intersects the Z-axis. For the given plane, the Z intercept is at z=8.
4Step 4: Sketch the graph of the plane
The graph will be a plane parallel to the x-y plane and passing through the point (0,0,8). It can be implemented by drawing an x-y graph, and a line parallel to the x-y plane which indicates z=8. The point where this line is present would be the z-intercept and the position of the plane.
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