I have been having a really rough time on my 3 homework problems tonight...I don't really understand vectors, so any help would be appreciated! Sorry about the no LaTeX, I don't know how to do the vector sign Anyway... 1.Given the Vectors U=2i(hat)-3j(hat)= <2,-3> and V=-i(hat)+4j(hat)= <-1,4>, find: a. U+V b. 2U-3V c. [tex]|V-U|[/tex] 2.Draw a sketch to find each of the following graphically. (P and Q are in the attachment) a. P+Q b. P-3Q c. -4P+4Q On this one, my friend told me just to basically draw a triangle for each one of the problems, and the added third line to complete the triangle would equal the resultant vector. Is this right? 3.An airplane pilor needs to fly to a point 1800 km due east in a time of 6.0 hours. If a steady wind is blowing at 60 km/h from due south towards due north, calculate the velocity of the plane relative to the air (specifying both magnitude and direction) needed to achieve the pilot's objective. I don't really know how side-winds affect flying objects being propelled at those speeds, some explanation on that would be appreciated to help solve the problem. Thanks for your time taken for the help!