Linear algebra- vectors?

A boat is traveling on a river in a SW direction at 10mph while a passenger is walking from the port to the starboard (from SE side to the NW side of the boat) at 2 mph. Find the velocity %26amp; speed of the passenger with respect to the shore.





--I began by drawing a vector from (0,0) in the 3rd quadrant (b/c its SW) with a length of 10. I have no idea where to go from here.

Linear algebra- vectors?
In every hour, the boat travels 10 miles southwest. In vector form, that is %26lt;- 5rt2,- 5rt2%26gt; (like you said, in quadrant 3).





Also in every hour, the person travels 2 miles NW. In vector form, that is %26lt;- rt2, rt2%26gt;, in quadrant 2.





Because the person vector overlays the boat vector, as the person is on the boat, you want to add these two vectors).


%26lt;- 5rt2,- 5rt2%26gt;+%26lt;- rt2, rt2%26gt; = %26lt;-6rt2, -4rt2%26gt;.





So the speed is the magnitude of that, sqrt (72+ 32) = sqrt (104). And to find velocity you need to find what direction the person is moving in, the angle between the vector above and the x or y axis. TO determine this take the arctan of -4rt2/-6rt2.

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