# Expected Distance of Unit Vectors

**Calculus**Level 3

Two unit vectors in two-dimensional space \(\hat{\textbf{a}}\) and \(\hat{\textbf{b}}\) are added together. The expected magnitude of the resulting vector \(\textbf{a+b}\) is equal to \(E.\) What is \(\lfloor100E\rfloor?\)

Also try Daniel Liu's Expected Distance on a Circle.