Question

Describe in words the region of \(R^{3}\) represented by the equation(s) or inequality.
\(x = 5\)

Answer 1

1) Concept:
The equation of the plane parallel to yz- plane is \(x = a\)
2) Given:
\(x = 5\)
3) Calculation:
The given equation is \(x = 5\)
The equation \(x = 5\) represents the set of all points in \(R^{3}\) whose x coordinate is 5.
That is \({(x, y, z) |\ x = 5, y \in R, z \in R}\)
This is a plane which is parellel to yz plane and five units in front of it.
Therefore,
\(x = 5\)
represents a plane in \(R^{3}\) parallel to yz plane and five units in front of it.
Conclusion:
\(x = 5\)
represents a plane in \(R^{3}\) parallel to yz plane and five units in front of it.