Direction cosines and ratios

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Direction ratios: $$a, b, c$$

Direction cosines: $$ l = \frac{a}{\sqrt{a^2 + b^2 + c^2}}, \quad m = \frac{b}{\sqrt{a^2 + b^2 + c^2}}, \quad n = \frac{c}{\sqrt{a^2 + b^2 + c^2}} $$

with $$ l^2 + m^2 + n^2 = 1 $$.

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