Euclidean Distancefor an Orthonormal System

• The Euclidean distance in a rectangular space is given by

D = ? (xb - xa)2 + (yb - ya)2 + (zb - za)2 .

• A straight line is the minimum distance path between a and b.

• The variables are linearly related by the parametric equations of a line.

• The equation of the line segment from a to b is given by

x = xa + (xb - xa) µ

y = ya + (yb - ya) µ

z = za + (zb - za) µ where the parameter µ is in [0 , 1].

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