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
