Determine the angle measure between vectors u and v: u = – 3i + 3j and v = 3i + 2j .

The angle between vectors is given by:
 cos (x) = (u.v) / (lul * lvl)
 We have then:
 u.v = (- 3i + 3j) * (3i + 2j)
 u.v = (-3 * 3) + (3 * 2)
 u.v = -9 + 6
 u.v = -3
 We look for the module of each vector:
 lul = root ((- 3) ^ 2 + (3) ^ 2) = 4.242640687
 lvl = root ((3) ^ 2 + (2) ^ 2) = 3.605551275
 Substituting values:
 cos (x) = (-3) / ((4.242640687) * (3.605551275))
 x = acos ((- 3) / ((4.242640687) * (3.605551275)))
 x = 101.31 degrees
 
 The angle measure between vectors and v is:
 x = 101.31 degrees

That they are numbers and related to each other.