Question

Surfaces in Three Dimensions Describe and sketch the surface represented by the given equation.

$x=4$.

Short answer

The equation $x=4$ represents the $x$ coordinate of the $xyz$ plane. The surface that is represented by the equation $x=4$, is the vertical plane that is parallel to the $yz$ plane and 4 units right of it. It is given by,

Step-by-step solution

Step 1. Given information.

Given: $x=4$

Step 2. Finding y,z coordinate values.

The surface in three-dimensional space can be made up of the points P$(x,y,z)$ . So, the given equation $x=4$ represents the coordinate of the point $P$ . From this, we can found that the coordinates of $y$and $z$ are zero.

Plot the point $(4,0,0)$ in the $xyz$ plane, we get

Step 3. Sketch the surface that is represented by the equation x=4.

In the graph, the surface that is represented by the equation $x=4$, is the vertical plane that is parallel to the $yz$ plane and 4 units right of it.