Moderate# Comparing Parallelograms

MVCALC-BQ8LEJ

Let ${\bf u}$ and ${\bf v}$ be two vectors of length two that make an angle of $30^{\circ}$ and form the adjacent sides of a parallelogram $P$.

Let ${\bf a}$ be a unit vector and let ${\bf b}$ be a vector of length $2$ so that ${\bf a}$ and ${\bf b}$ form the adjacent sides of a parallelogram $R$ whose area is equal to the area of $P$.

What angle do ${\bf a}$ and ${\bf b}$ make?