Question:
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
Solution:
If a line has direction ratios of −18, 12, and −4, then its direction cosines are
$\frac{-18}{\sqrt{(-18)^{2}+(12)^{2}+(-4)^{2}}}, \frac{12}{\sqrt{(-18)^{2}+(12)^{2}+(-4)^{2}}}, \frac{-4}{\sqrt{(-18)^{2}+(12)^{2}+(-4)^{2}}}$
i.e., $\frac{-18}{22}, \frac{12}{22}, \frac{-4}{22}$
$\frac{-9}{11}, \frac{6}{11}, \frac{-2}{11}$
Thus, the direction cosines are $-\frac{9}{11}, \frac{6}{11}$, and $\frac{-2}{11}$.
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