Question

If a line makes angles $90°$, $135°$, and $45°$ with the $\mathrm{x}$, $\mathrm{y}$ and, $\mathrm{z}$ axis respectively, find its direction cosines?

Answer 1

Determine direction cosines:

Take direction cosines as $\mathrm{l}$, $\mathrm{m}$, $\mathrm{n}$.

The given angles are $90°$, $135°$, $45°$

$$\begin{gathered} \therefore \mathrm{l}=\cos \left(90°\right) \\ =0 \end{gathered}$$

$$\begin{gathered} \mathrm{m}=\cos \left(135°\right) \\ =-\frac{1}{\sqrt{2}} \end{gathered}$$

$$\begin{gathered} \mathrm{n}=\cos \left(45°\right) \\ =\frac{1}{\sqrt{2}} \end{gathered}$$

Hence, the direction cosines are $0$, $-\frac{1}{\sqrt{2}}$ , $\frac{1}{\sqrt{2}}$.