Question

If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?

Answer 1

$$\begin{gathered} \mathrm{If}\mathrm{a}\mathrm{line}\mathrm{has}\mathrm{direction}\mathrm{ratios}\mathrm{proportional}\mathrm{to}2,-1,\mathrm{and}-2,\mathrm{then}\mathrm{its}\mathrm{direction}\mathrm{cosines}\mathrm{are} \\ \frac{2}{\sqrt{{\left(2\right)}^2+\left(-1\right)+{\left(-2\right)}^2}},\frac{-1}{\sqrt{{\left(2\right)}^2+\left(-1\right)+{\left(-2\right)}^2}},\frac{-2}{\sqrt{{\left(2\right)}^2+\left(-1\right)+{\left(-2\right)}^2}} \\ =\frac{2}{3},-\frac{1}{3},-\frac{2}{3} \\ \mathrm{Thus},\mathrm{the}\mathrm{direction}\mathrm{cosines}\mathrm{are}\frac{2}{3},-\frac{1}{3},-\frac{2}{3}. \end{gathered}$$