Case-Study 1: Read the following passage and answer the questions given below. A cricket match is organized between two Clubs A and B for which a team from each club is chosen. Remaining players of Club A and Club B are respectively sitting on the plane represented by the equation
$\overrightarrow{\mathrm{r}}\cdot (2\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})=3\text{ and }\overrightarrow{\mathrm{r}}\cdot (\hat{\mathrm{i}}+3\mathrm{j}+2\hat{\mathrm{k}})=8$

Answer the following questions using the above information.
(i) The Cartesian equation of the plane on which players of Club A are seated is
(a) 2x - y + z = 3                       (b) 2x - y + 2z = 3
(c) 2x - y + z = - 3                      (d) x - y + z = 3
(ii) Which of the following is a player of Club B?
(a) Player sitting at (1, 2, 1)
(b) Player sitting at (0, 1, 2)
(c) Player sitting at (1, 4, 1)
(d) Player sitting at (1, 1, 2)
(iii) The distance of the plane, on which players of Club B are seated, from the origin
is
$\text{ (a) }\frac{8}{\sqrt{14}}\text{ units }$  $\text{ (b) }\frac{6}{\sqrt{14}}\text{ units }$
$\text{ (c) }\frac{7}{\sqrt{14}}\text{ units }$       $\text{ (d) }\frac{9}{\sqrt{14}}\text{ units }$