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Find the point where the perpendicular drawn from the point (2, 4, −1) meets the line x + 5 = (1/4)(y + 3) = (−1/9)(z − 6).

1. (−4, 1, −3)
2. (4, −1, −3)
3. (−4, −1, 3)
4. (4, −1, −3)

Correct answer: (−4, 1, −3)

Solution

Points on the line are (-5+t, -3+4t, 6-9t) with direction (1,4,-9). Requiring the vector from P(2,4,-1) to be perpendicular to (1,4,-9) gives t=1, so the foot is (-4,1,-3).

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