Question

Label any intercepts and sketch a graph of the plane. $$ x=5 $$

Short answer

The plane \(x = 5\) intersects the x-axis at the point (5, 0, 0). It's a plane parallel to the yz-plane and 5 units away from the origin along the positive x-axis. It only has one intercept, and doesn't intersect the y-axis or z-axis at all.

Step-by-step solution

Identify the Plane

Given equation of the form \(x = k\), represents a vertical plane. It’s parallel to the yz-plane. In this case, the given equation is \(x = 5\), so the plane is 5 units away from the origin along the positive x-axis since 5 is positive.

Sketch the Plane

To sketch this, start by drawing coordinate axes. Mark a point on the positive x-axis 5 units away from the origin. Now draw a vertical plane parallel to the yz-plane passing through this point you've marked.

Label the Intercepts

Since the plane is parallel to the yz-plane, it won't intersect the y-axis or z-axis. It only intersects the x-axis at the point (5, 0, 0). So this point is the only intercept for this plane.