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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?

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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.

The distance between the points P(2, 1, 0) and Q(3, 3, 0) is:

Learn how to calculate the distance between points P(2, 1, 0) and Q(3, 3, 0) using the 3D distance formula. This step-by-step solution covers key concepts in analytic geometry and applies the Pythagorean theorem in three dimensions. Ideal for high school students in Grades 9-12.

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