Can somebody help me with the following two problems?
1. Find a value of a such that the vector <a, 1,1> makes an angle of 45 degrees with the vector <1,2,1> or show that no such a exists.
---I started by using theta = arccos (u*v)/(absu*absv) must equal (sqrt2)/2 and attempting to solve from there...but I'm not sure if that's the best way to proceed.
2. Let u = 3i + j; v = 5i - 2j; and w = i - j. Find scalars, a and b such that u = av +bw.
I have no idea how to proceed with this one.
I would greatly appreciate any help!!!