The boat question on the test.

A small boat is traveling at a speed of 5 mph in relative to the water. The boat is travelling in flowing water with a current velocity given by –3, –3 . In what direction should the boat head to travel due east? (Represent the direction with a unit vector.) 

10:04AM&10:16AM
Can you explain how to solve the boat question yet?


2:21PM
Ok I think I finally woke up. Is this problem really as simple as it seems? Is the answer really only the unit vector form of any vector that when added to <-2,-4> produces a vector of form <a,0> with a >0?

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Yep.  This is actually a hugely important problem,  faced every day by people navigating aircraft or boats.  The direction that the boat is facing, is called the heading--in your case it should have been the direction of the vector <3,4> (since this has length 5), which is give by the unit vector <3/5,4/5>. The track or course over ground or course bearing is the direction you are actually moving toward, in this case given by the unit vector <1,0>.  To compensate for the effect of an ocean current or wind it's often necessary to have a heading that is in a different direction than your intended track.  Here's a wiki article on the subject, I'll update this page if I find a better link. and here's a link to a navigation article.