The Cartesian equation of the passing through the point $(1, -3, 2)$ and parallel to the line $\vec{r} = (2+\lambda)\hat{i} + \lambda\hat{j} + (2\lambda-1)\hat{k}$ is

$\frac{x-1}{1} = \frac{y+3}{1} = \frac{z-2}{2}$

The correct answer is Option (4) → $\frac{x-1}{1} = \frac{y+3}{1} = \frac{z-2}{2}$ ##

Given line is

$\vec{r} = (2+\lambda)\hat{i} + \lambda\hat{j} + (2\lambda-1)\hat{k}$

$\vec{r} = (2\hat{i} - \hat{k}) + \lambda(\hat{i} + \hat{j} + 2\hat{k})$

which is of the form $\vec{r} = \vec{a} + \lambda\vec{b}$

$∴$ Required line is

$\frac{x-1}{1} = \frac{y+3}{1} = \frac{z-2}{2}$