Let P = (10, -2, -1). Let Q be the foot of the perpendicular from R = (1, 7, 6) to the line passing through A = (2, -5, 11) and B = (-6, 7, -5). Find the length of segment PQ.

Correct answer: 14

Solution

The direction vector of AB simplifies to (2, -3, 4). Write the line as (2-8t, -5+12t, 11-16t) and find t such that (point - R) is perpendicular to the direction. Solving gives a specific point Q, then |PQ| is computed.

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