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.

Image credit: Wikipedia P.Fraundorf
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