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# Monitoring Currents

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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