Direction Cosines
If l, m, n are direction cosines of a line, then l² + m² + n² equals
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About This Question
- Subject
- mathematics
- Chapter
- three dimensional geometry
- Topic
- direction cosines
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
1
- Definition: Direction cosines l,m,n are the cosines of the angles α,β,γ that a line makes with the positive x,y,z axes respectively: l=cosα,m=cosβ,n=cosγ.
- Vector Analysis: If r is a unit vector along the line, it can be expressed as r=li^+mj^+nk^.
- Magnitude: Since ∣r∣=1, we have l2+m2+n2=1.
- Result: Squaring both sides gives l2+m2+n2=1. This is a fundamental property of direction cosines.
This easy difficulty mathematics question is from the chapter three dimensional geometry, covering the topic of direction cosines. It appeared in the 2025 exam.
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