The perpendicular distance from a point P with position vector p to a line r = a + λb is

1. Decompose (p - a) into components parallel and perpendicular to b. 2. The perpendicular component has magnitude |p - a| sin θ. 3. Equivalently, |(p - a) × b| = |p - a| · |b| sin θ, so |p - a| sin θ = |(p - a) × b| / |b|. 4. This is the perpendicular distance from P to the line. _Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.3_