Direction cosines and the identity l² + m² + n² = 1 (l = cos α, m = cos β, n = cos γ; l² + m² + n² = 1)
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l = cos α, m = cos β, n = cos γ; l² + m² + n² = 1
What each symbol means
| Symbol | What it stands for |
|---|---|
| a,b,c | Direction ratios (proportional to l,m,n) |
| l,m,n | Direction cosines |
| α,β,γ | Angles with x, y, z axes respectively |
When to use this
For direction ratios (a,b,c): l = a/√(a²+b²+c²), etc. The identity l²+m²+n²=1 follows from the unit vector.