In this question, i is a unit vector due east and j is a unit vector due north. Distances are measured in kilometres and time is measured in hours. Point \(P\) has position vector \(2 \mathbf{i}+5 \mathbf{j}\) relative to an origin \(O\). At 1300 , boat \(A\) sails from point \(P\) with velocity vector \(8 \mathbf{i}+8 \mathbf{j}\). (a) Find the position vector of \(A\) at the end of 2 hours of sailing. [1] (b) Write down the position vector of \(A\) at the end of \(t\) hours of sailing. [1] (c) Point \(Q\) has position vector \(20 \mathbf{i}+8 \mathbf{j}\) relative to the origin \(O\). At 1500 , boat \(B\) sails from point \(Q\) on a bearing of \(300^{\circ}\) with a constant speed of \(5 \sqrt{3}\). Find the position vector of \(B\) at 1700. [3] (d) Find the distance between the two boats at 1700.

2026 - M/J - 0606/22 | Q7

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In this question, i is a unit vector due east and j is a ...