The distance between two points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ in three-dimensional space is:

3D distance formula extends Pythagoras into three dimensions: the distance is the square root of the sum of squared coordinate differences. Derivation: project the segment $PQ$ onto each axis to get the leg lengths $|x_2 - x_1|$, etc. Apply Pythagoras twice. Option B is the **Manhattan** (taxicab) distance, useful in some lattice problems but not the Euclidean answer.