Let $P$ be the plane passing through the intersection of the planes $\vec{r} \cdot(\hat{i}+3 \hat{j}-\hat{k})=5$ and $\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=3$, and the point $(2,1,-2)$. Let the position vectors of the points $X$ and $Y$ be $\hat{i}-2 \hat{j}+4 \hat{k}$ and $5 \hat{i}-\hat{j}+2 \hat{k}$ respectively. Then the points