To find the equation of a line that is parallel to the y-axis and passes through the point $P(3, 2, 0)$ in three-dimensional space, you need to fix the $x$- and $z$-coordinates to those of the given point and let the $y$-coordinate vary.

Since the line is parallel to the y-axis:

• $x$ will remain constant at 3.
• $z$ will remain constant at 0.
• $y$ will vary.

The parametric equations of the line can be written as: $x = 3, \quad y = t, \quad z = 0$ where $t$ is a parameter that can take any real value.

Thus, the equation of the line is:

$\boxed{x = 3, \quad z = 0}$

This describes a line parallel to the y-axis passing through the point $(3, 2, 0)$.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What is the equation of a line parallel to the z-axis through the point $(3, 2, 0)$?
2. How would you describe a line parallel to the x-axis passing through the point $(3, 2, 0)$?
3. How can you determine if two lines in 3D space are parallel?
4. What is the equation of a line parallel to the y-axis through a different point, say $(1, 4, -2)$?
5. How do you find the intersection of two lines in 3D space?

Tip: In 3D geometry, when given a line parallel to one of the axes, only the coordinate corresponding to that axis is allowed to vary; the others remain fixed at the point's coordinates.