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Precalculus : Building Concepts and Connections

In this set of exercises, you will use vectors and dot products to study real-world problems.

Distance Two tourboats, Swan and Dolphin, depart from a lighthouse, with one directly behind another. However, after some time, Swan strays off course and ends up at position \langle 1,2\rangle , relative to the lighthouse. The other boat, Dolphin, stays on course with a position vector $\langle 5,3\rangle,$ relative to the lighthouse. What is the shortest distance that Swan must travel to get back on the same course as Dol-

phin, assuming that Dolphin kecps traveling in its current direction? All positions are given in miles. Round your answer to two decimal places.

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