Part of V3D-02 — Three-Dimensional Geometry

Distance from a Point to a Line

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The distance from point P(p) to the line r = a + lambdab is: d = |(p - a) x b| / |b|. Alternatively, find the foot of perpendicular by writing a general point on the line as Q = a + lambdab, setting PQ . b = 0 (perpendicularity condition), solving for lambda, then computing |PQ|. The parametric method is more versatile as it also gives the coordinates of the foot.

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