In this question, all distances are measured in kilometres.
2 deep sea ocean current monitors, A and B, have position vectors (-1, 7, k) and (4, 1, 10) respectively, relative to a fixed origin. Given that the distance from A to B is \(5\sqrt{5}\)km,
a) Find the possible values of the constant k.
[3 marks]
b) For the larger value of k, find the unit vector in the direction of \(\overrightarrow{\text{OA}}\)
[3 marks]
