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