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The angle ϕ between a line with direction b and a plane with normal n satisfies
Acos ϕ = b · n / (|b||n|)
Bsin ϕ = b · n / (|b||n|)
Ctan ϕ = b · n
Dcos ϕ = b × n
Answer & Solution
Correct answer: B. sin ϕ = b · n / (|b||n|)
1. Let α be the angle between line direction b and plane normal n.
2. Then cos α = (b · n) / (|b| · |n|).
3. The angle between the line and the plane is ϕ = 90° - α.
4. Therefore sin ϕ = cos α = (b · n) / (|b| · |n|).
_Source: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.10_
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