Home › UP Board Class 12 › Mathematics › Three Dimensional Geometry › The foot of the perpendicular from origin to the…
The 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: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.9_
Related questions
The image of the point (1, 2, 3) in the plane x + y + z = 0 isThe line through the origin with direction ratios (1, 1, 1) meets the plane x + y + z = 6 A line has direction ratios (1, 1, 2) and meets the plane x - y + z = 0. The angle ϕ betweThe plane through the points (1,1,0), (1,0,1) and (0,1,1) has equationThe equation of a plane parallel to x + 2y - 3z = 5 and passing through (1, 1, 1) isThe shortest distance between r = (1,2,3) + λ(2,3,4) and r = (2,4,5) + μ(3,4,5) isThe line r = (2, -1, 4) + λ(3, 0, 2), expressed in symmetric Cartesian form, isThe distance between the parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z = 5 is