Vector equation for x-axis is $\vec{r} = \lambda \hat{i}$ where $x = \lambda$. Let a point P(λ, 0, 0) is on the x-axis perpendicular to the given point A(0, 1, 2) then $\overrightarrow{AP}$ is perpendicular to $\lambda \hat{i}$.$\overrightarrow{AP} \cdot \lambda \hat{i} = 0$ where $\overrightarrow{AP} = \lambda \hat{i} - \hat{j} - 2 \hat{k}$$(\lambda \hat{i} - \hat{j} - 2 \hat{k}) \cdot (\lambda \hat{i} + 0 \hat{j} + 0 \hat{k}) = 0$$\lambda^2 = 0$$\lambda = 0$, so the foot of the perpendicular drawn from the point (0, 1, 2) is (0, 0, 0).