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Question 350011
JEE Mathematics · Hard

Three Dimensional Geometry: JEE Advanced MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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JEE AdvancedHardQuestion 350011

Question

The foot of perpendicular from origin to the plane 2x+3y−4z=29 is:
  1. A
    (2, 3, −4)
    Correct
  2. B
    (2, 3, −4) (scaled to fit)
  3. C
    Cannot determine
  4. D
    (4, 6, −8)

Correct answer

(2, 3, −4)

Explanation

The foot of perpendicular from origin to plane 2x+3y−4z=29: The foot lies on the normal through origin: (x,y,z) = t(2,3,−4). Substituting: 2(2t)+3(3t)−4(−4t) = 29 → 4t+9t+16t=29 → 29t=29 → t=1. Foot = (2,3,−4).

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