The locus of xy + yz = 0 is

The correct option is **A pair of perpendicular planes**.

To find the locus of the given equation:
$$xy+yz=0$$

We can factor out the common term $y$ from the equation:
$$y(x+z)=0$$

This gives us two separate equations representing the components of the locus:
1) $y=0$
2) $x+z=0$

In three-dimensional space, both of these equations represent planes:
- The equation $y=0$ represents the $zx$-plane. Its normal vector is $\overrightarrow{n_1}=(0,1,0)$.
- The equation $x+z=0$ represents a plane passing through the y-axis. Its normal vector is $\overrightarrow{n_2}=(1,0,1)$.

To determine the geometric relationship between these two planes, we can calculate the dot product of their normal vectors:
$$\overrightarrow{n_1}·\overrightarrow{n_2}=(0)(1)+(1)(0)+(0)(1)=0$$

Since the dot product of the normal vectors is zero, the two normal vectors are perpendicular to each other. Consequently, the planes themselves are perpendicular.
Thus, the locus represented by $xy+yz=0$ is a pair of perpendicular planes.