# 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.

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