alleryThe foot of the perpendicular from origin to the plane 2x + 3y - 6z = 14 is
A(4/7, 6/7, -12/7)
B(2, 3, -6)
C(2/7, 3/7, -6/7)
D(1, 1, 1)
Answer & Solution
Correct answer: A. (4/7, 6/7, -12/7)
1. The foot lies along the line from origin in the direction of the normal (2, 3, -6).
2. Parametrize: P = t(2, 3, -6).
3. Substitute into the plane: 2(2t) + 3(3t) - 6(-6t) = 14 → 49t = 14 → t = 2/7.
4. Foot: (2t, 3t, -6t) = (4/7, 6/7, -12/7).
_Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.9_
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