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The question asks to find the shortest distance between two points, \( P(1 \text{ m}, 4 \text{ m}, 3 \text{ m}) \) and \( Q(-2 \text{ m}, -1 \text{ m}, 2 \text{ m}) \).

The shortest distance between two points in 3D space is given by the formula for the Euclidean distance:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
\]

Substitute the coordinates of points \( P(1, 4, 3) \) and \( Q(-2, -1, 2) \) into the formula:

\[
d = \sqrt{((-2 - 1)^2) + ((-1 - 4)^2) + ((2 - 3)^2)}
\]
\[
d = \sqrt{(-3)^2 + (-5)^2 + (-1)^2}
\]
\[
d = \sqrt{9 + 25 + 1}
\]
\[
d = \sqrt{35}
\]

Thus, the shortest distance between the two points is \( \sqrt{35} \) meters.

The correct answer is option (4): \( \sqrt{35} \) meters.

Would you like further details or have any other questions?

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Here are 5 related questions for deeper understanding:

1. How is the Euclidean distance formula derived?
2. What is the difference between 2D and 3D distance calculations?
3. How can the distance formula be applied in physics to calculate displacement?
4. What are some practical applications of finding distances in 3D space?
5. How do you calculate distances in non-Euclidean geometries?

**Tip:** Always square the differences in coordinates carefully to avoid sign errors in distance calculations!

The shortest distance between the point P(1m, 4m, 3m) and Q(-2m, -1m, 2m) is:

Learn how to calculate the shortest distance between two points in 3D space using the Euclidean distance formula. This step-by-step solution covers points P(1m, 4m, 3m) and Q(-2m, -1m, 2m), applying the Pythagorean theorem in a 3D context.

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