Expected Distance of Unit Vectors

Calculus Level 3

Two unit vectors in two-dimensional space a^\hat{\textbf{a}} and b^\hat{\textbf{b}} are added together. The expected magnitude of the resulting vector a+b\textbf{a+b} is equal to E.E. What is 100E?\lfloor100E\rfloor?


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

Image credit: Wikipedia P.Fraundorf
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