Question

Find the intercepts and sketch the graph of the plane. $$ x=5 $$

Short answer

The given equation represents a plane that intersects the x-axis at (5,0,0). It's parallel to the yz-plane. The sketch would depict a flat surface parallel to the yz-plane, passing through the 5th point on the x-axis.

Step-by-step solution

Identifying the plane

The given equation represents a plane parallel to the yz-plane. The plane equation is x = 5, indicating the plane crosses the x-axis at point (5, 0, 0).

Sketching the plane

Sketch the 3D coordinate axes. Draw the plane at the fifth mark on the positive side of the x-axis, such that the plane is parallel to the yz-plane.

Indicating the intercept

The plane intersects the x-axis at (5, 0, 0). Mark this point on the sketch.