Find the point of intersection of the line $\overrightarrow{r} = \left(\overrightarrow{j} - \overrightarrow{k}\right) + \lambda \left(2 \hat{i} - \hat{j} + \hat{k}\right)$ and the $xz$ plane.
Equation of given line in vector form: $\;$ $\overrightarrow{r} = \left(\overrightarrow{j} - \overrightarrow{k}\right) + \lambda \left(2 \hat{i} - \hat{j} + \hat{k}\right)$
$\therefore$ $\;$ Equation of given line in cartesian form is: $\;$ $\dfrac{x}{2} = \dfrac{y - 1}{-1} = \dfrac{z + 1}{1}$ $\;\;\; \cdots \; (1)$
The given line meets the $xz$ plane i.e. $\;$ $y = 0$
Substituting $y = 0$ in equation $(1)$ gives
$\dfrac{x}{2} = 1$ $\implies$ $x = 2$
$\dfrac{z + 1}{1} = 1$ $\implies$ $z = 0$
$\therefore$ $\;$ The point of intersection of the given line and the plane is $\;$ $\left(2, 0, 0\right)$