Question

The total number of straight lines equally inclined with the coordinate axis is ____________.

Answer 1

for any equally inclined line, α = β = γ (i.e direction cosines are same)
i.e cosα = cosβ = cosγ
i.e ​cos²α + cos²β + cos²γ = 1
i.e 3 cos²α = 1
$$\begin{gathered} \mathrm{i}.\mathrm{e}{\cos }^2\alpha =\frac{1}{3} \\ \mathrm{i}.\mathrm{e}\cos \alpha =\pm \frac{1}{\sqrt{3}} \\ \cos \beta =\pm \frac{1}{\sqrt{3}}\mathrm{and}\cos \gamma =\pm \frac{1}{3} \end{gathered}$$
∴ Total 8 straight line segments are possible which are equally inclined to coordinate axes.