`u = 5i + 5j, v = -6i + 6j` Find the angle theta between the vectors.

We want to get the angle, `\theta` between vectors u = 5i + 5j and v = -6i + 6j. By definition, the angle  between two vectors is defined as follows (u and v are two vectors):

`cos (\theta) = ( v \cdot u)/(||v|| ||u||)` .Hence, `\theta = cos^(-1)(v \cdot u)/(||v|| ||u||)` .

`||v|| = \sqrt(5^2 + 5^2) = \sqrt(50) = 5\sqrt(2)` .

`||u|| = \sqrt((-6)^2 + 6^2) = \sqrt(72) = 6\sqrt(2)` .

`v \cdot u = (5*-6) + (5*6) = 0` .

Hence, `\theta = cos^(-1)(0) = \pi/2` .