alleryThe image of the point (1, 2, 3) in the plane x + y + z = 0 is
A(-1, -2, -3)
B(-1, 0, 1)
C(-3, -2, -1)
D(1, -2, -3)
Answer & Solution
Correct answer: C. (-3, -2, -1)
1. The plane has normal n = (1, 1, 1) (unnormalised) and passes through the origin.
2. The projection of (1, 2, 3) onto n is ((1+2+3)/3)(1, 1, 1) = 2(1, 1, 1).
3. Image = point - 2 × projection = (1, 2, 3) - (4, 4, 4).
4. So image = (-3, -2, -1).
_Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.9_
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