Let M(k,4,k−1) be a point such that its distance from N(2,−1,3) is 10 units.
(i) Obtain the quadratic equation in k implied by the distance condition.
(ii) Solve the equation to find the possible values of k and hence the corresponding coordinates of M.
(iii) If M is also required to satisfy the plane 2x+y−z=7, determine which of the coordinates obtained in part (ii) is acceptable and justify your answer.