alleryA line has direction ratios (1, 1, 2) and meets the plane x - y + z = 0. The angle ϕ between them satisfies
Acos ϕ = 2/(√6 · √3)
Btan ϕ = 1/3
Cϕ = 90°
Dsin ϕ = 2/(√6 · √3)
Answer & Solution
Correct answer: D. sin ϕ = 2/(√6 · √3)
1. Direction vector b = (1, 1, 2); plane normal n = (1, -1, 1).
2. Dot product b · n = 1 - 1 + 2 = 2.
3. Magnitudes |b| = √6, |n| = √3.
4. sin ϕ = (b · n) / (|b| |n|) = 2/(√6 · √3) = 2/√18.
_Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.10_
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