Problem 10.2#17

 Hello Dr. Taylor,
I am can't figure out what to multiply the first part of
number 17 by to get half its length and it in the opposite direction. I got
the unit vector but can't figure out the proper scalar please help.

(click on image to enlarge)
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Well, for part 1 you're doing good things with dividing by the length to find a unit vector, but you're making it harder than it needs to be.  To get a vector half the length of u, you just have to multiply it by 1/2.  And to get it going in the opposite direction you just have to multiply it by -1. You *don't* need to divide by the length of u.

For part 2, though, you need to get a vector of exactly length 3 pointing in the direction of v, so you're doing exactly the right thing by computing the unit vector v/|v| and then multiplying by 3