alleryThe line through the origin with direction ratios (1, 1, 1) meets the plane x + y + z = 6 at
A(1, 1, 1)
B(2, 2, 2)
C(3, 3, 3)
D(6, 0, 0)
Answer & Solution
Correct answer: B. (2, 2, 2)
1. Parametrize the line: (x, y, z) = (t, t, t).
2. Substitute into the plane equation: t + t + t = 6.
3. Solve: 3t = 6, so t = 2.
4. Intersection point: (2, 2, 2).
_Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.3.1_
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