The coordinates of the foot of the perpendicular drawn from the origin to the plane 2x − 3y + 4z − 6 = 0 are:
The coordinates of the foot of the perpendicular drawn from the origin to the plane 2x − 3y + 4z − 6 = 0 are:
- A. (12/29, −18/29, 24/29)
- B. (2/29, −3/29, 4/29)
- C. (12/29, 18/29, 24/29)
- D. (6/29, −9/29, 12/29)
Answer: A) (12/29, −18/29, 24/29)
Explanation: Normal DRs are 2, −3, 4. Line from origin is x/2 = y/−3 = z/4 = k. Substitute into plane: 2(2k) − 3(−3k) + 4(4k) = 6 → 4k + 9k + 16k = 6 → 29k = 6 → k = 6/29. Point is (12/29, −18/29, 24/29).
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