The equation xy = 0 in three dimensional space is represented by

The correct option is "two plane are right angles".

To understand why this is correct, let's analyze the given equation in three-dimensional space (${ℝ}^3$):

$xy=0$

For the product of two real numbers $x$ and $y$ to be zero, at least one of the numbers must be zero. This gives us two possible cases:
1. $x=0$
2. $y=0$

In three-dimensional Cartesian coordinate space $(x,y,z)$:
- The equation $x=0$ represents the set of all points where the x-coordinate is zero, which is the y-z plane.
- The equation $y=0$ represents the set of all points where the y-coordinate is zero, which is the x-z plane.

Thus, the equation $xy=0$ represents the union of these two planes (the y-z plane and the x-z plane).

Now, let's look at the relationship between these two planes:
- The normal vector to the plane $x=0$ is $\hat{i}=(1,0,0)$.
- The normal vector to the plane $y=0$ is $\hat{j}=(0,1,0)$.

Taking the dot product of these two normal vectors to find the angle between the planes:

$\hat{i}·\hat{j}=1·0+0·1+0·0=0$

Since the dot product of their normal vectors is zero, the two planes are perpendicular to each other. Therefore, the equation represents two planes at right angles.