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The perpendicular distance from a point P with position vector p to a line r = a + λb is
A|(p - a) · b| / |b|
B|(p + a) × b|
C|p - a|
D|(p - a) × b| / |b|
Answer & Solution
Correct answer: D. |(p - a) × b| / |b|
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: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.3_
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