3d Geometry

Let $\ell_1$ and $\ell_2$ be the lines $\vec{r}_1=\lambda(\hat{i}+\hat{j}+\hat{k})$ and $\vec{r}_2=(\hat{j}-\hat{k})+\mu(\hat{i}+\hat{k})$, respectively. Let $X$ be the set of all the planes $H$ that contain the line $\ell_1$. For a plane $H$, let $d(H)$ denote the smallest possible distance between the points of $\ell_2$ and $H$. Let $H_0$ be a plane in $X$ for which $d\left(H_0\right)$ is the maximum value of $d(H)$ as $H$ varies over all planes in $X$.


Match each entry in List-I to the correct entries in List-II.



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List - I	List - II
(P) The value of $d\left(H_0\right)$ is	(1) $\sqrt{3}$
(Q) The distance of the point $(0,1,2)$ from $H_0$ is	(2) $\frac{1}{\sqrt{3}}$
(R) The distance of origin from $H_0$ is	(3) 0
(S) The distance of origin from the point of intersection of planes $y=z, x=1$ and $H_0$ is	(4) $\sqrt{2}$
	(5) $\frac{1}{\sqrt{2}}$

The correct option is: