Question

The equations of a line passing through point (–2, 3, 4) and equally inclined with the coordinate axes OX, OY and OZ are ______________.

Answer 1

Since for equally inclined line with the coordinate axes OX, OY, and OZ direction ratios is of the form (k, k, k) or (1, 1, 1)

Since line passes through (−2, 3, 4)

i.e. x₁ = −2, y₁ = 3, z₁ = 4 and a = 1, b = 1, c = 1

$$\begin{gathered} \therefore \mathrm{equation}\mathrm{of}\mathrm{line}\mathrm{is}\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c} \\ \mathrm{i}.\mathrm{e}.\frac{x+2}{1}=\frac{y-3}{1}=\frac{z-4}{1} \end{gathered}$$