Find the vector and cartesian equations of the plane passing through the points $\left(2,5,-3\right),\left(-2,-3,5\right)$ and $\left(5,3,-3\right)$. Also, find the point of intersection of this plane with the line passing through points $\left(3,1,5\right)$ and $\left(-1,-3,-1\right)$.
OR
Find the equation of the plane passing through the intersection of the planes $\overrightarrow{\mathit{r}}\cdot \left(\hat{\mathit{i}}+\hat{\mathit{j}}+\hat{\mathit{k}}\right)=1$ and $\overrightarrow{\mathit{r}}\cdot \left(2\hat{\mathit{i}}+3\hat{\mathit{j}}-\hat{\mathit{k}}\right)+4=0$ and parallel to $\mathrm{x}$-axis. Hence, find the distance of the plane from $\mathrm{x}$-axis.