To find the distance between points $P(2, 1, 0)$ and $Q(3, 3, 0)$, we use the 3-dimensional distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$

For $P(2, 1, 0)$ and $Q(3, 3, 0)$:

1. $x_1 = 2$, $y_1 = 1$, $z_1 = 0$
2. $x_2 = 3$, $y_2 = 3$, $z_2 = 0$

Substitute these values:

$d = \sqrt{(3 - 2)^2 + (3 - 1)^2 + (0 - 0)^2}$ $d = \sqrt{1^2 + 2^2 + 0^2}$ $d = \sqrt{1 + 4 + 0}$ $d = \sqrt{5}$

So, the distance is $\sqrt{5}$.

Would you like further details, or do you have any questions?

Here are some related questions for further exploration:

1. How would the formula change if there were four dimensions?
2. Can the distance formula be applied to find distances on a plane, rather than in 3D?
3. What would the distance be if the points had different $z$-coordinates?
4. How can this formula be derived from the Pythagorean theorem?
5. Are there other ways to calculate distance between points in different coordinate systems?

Tip: Always double-check each coordinate substitution to avoid small calculation errors.