Find the vector and Cartesian equations of the plane passing

Question:

Find the vector and Cartesian equations of the plane passing through the point $(3,-1,2)$ and parallel to the lines

$\overrightarrow{\mathrm{r}}=(-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\lambda(2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}-\hat{\mathrm{k}})$ and $\overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\mu(-5 \hat{\mathrm{i}}+4 \hat{\mathrm{j}})$.

Solution: