The length of projection of the line segment joining the points $\left(1,0,–1\right)$ and $\left(–1,2,2\right)$ on the plane $x+3y–5z=6$ is equal to

$L_1: \overrightarrow{r}=3\hat{i}-\hat{j}+2\hat{k}+\lambda \left(2\hat{i}+4\hat{k}-\hat{k}\right)$

$L_2: \overrightarrow{r}=\hat{i}+\hat{j}-3\hat{k}+\mu \left(4\hat{i}+2\hat{j}+4\hat{k}\right)$

$L_3: \overrightarrow{r}=3\hat{i}+2\hat{j}-2\hat{k}+t\left(2\hat{i}+\hat{j}+2\hat{k}\right)$

Then, which one of the following pair(s) is/are in the same plane?