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

Answer:

The angle measure between vectors and v is:

x = 101.31 degrees