Let ℓ _ 1 and ℓ _ 2 be the lines → r 1 = λ( ^ i + ^ j + ^ k ) and →...

Let ${ℓ}_{1} and${ℓ}_{2}$be the lines$\overset{\to}{r}1 = \lambda\left(\overset{^}{i} + \overset{^}{j} + \overset{^}{k}\right)$and$\overset{\to}{r}2 = \left(\overset{^}{j} - \overset{^}{k}\right) + \mu\left(\overset{^}{i} + \overset{^}{k}\right)$, respectively, Let$X$be the set of all the planes$H$that contain the line${ℓ}_{1}$. For a plane$H$, let$d\left(H\right)$denote the smallest possible distance between the points of${ℓ}_{2}$and$H$. Let${H}_{0}$be a plane in$X$for which$d\left({H}_{0}\right)$is the maximum value of$d\left(H\right)$as$H$varies over all planes in$X$.</p><p>Match each entry in List-I to the correct entries in List-II.</p><table border="1" cellpadding="1" cellspacing="1" style="width: 500px;"> <tbody> <tr> <td> </td> <td>List-I</td> <td> </td> <td>List-II</td> </tr> <tr> <td>$\left(P\right)$</td> <td>The value of$d\left({H}_{0}\right)$is</td> <td>\left(1\right)$ $\sqrt{3}$ \left(Q\right)$</td> <td>The distance of the point \left(0, 1, 2\right)$ from ${H}_{0}$ is \left(2\right)$</td> <td>$\dfrac{1}{\sqrt{3}}$</td> </tr> <tr> <td>\left(R\right)$ The distance of origin from ${H}_{0}$ is \left(3\right)$</td> <td>$0$</td> </tr> <tr> <td>\left(S\right)$ The distance of origin from the point of
intersection of planes $y = z, x = 1$ and ${H}_{0}$ is \left(4\right)$</td> <td>$\sqrt{2}$</td> </tr> <tr> <td> </td> <td> </td> <td>\left(5\right)$ $\dfrac{1}{\sqrt{2}}$

The correct option is