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Part 1: Types of intersections

Consider the equations $x = 5$ , $y = -2$ , and $z = 4$ in $\mathbb{R}^3$ .

The set of points satisfying the equation $x = 5$ is a

The set of points satisfying the equation $y = -2$ is a

The set of points satisfying the equation $z = 4$ is a

The set of points satisfying both $x = 5$ and $y = -2$ is a

The set of points satisfying both $x = 5$ and $z = 4$ is a

The set of points satisfying both $y = -2$ and $z = 4$ is a

The set of points satisfying $x = 5$ , $y = -2$ , and $z = 4$ is a

Part 2: One plane

Part 3: Two planes

Part 4: Three planes

You can earn partial credit on this problem.