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Monitoring Currents

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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]

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