Vector and Area

Level pending

Let \(N\) be the area of the plane represented by the vector equation \[\boldsymbol{r} (u, v) = < v,\ u-2v,\ 1-2u+v >,\] where \( 0 \leq u \leq 1\) and \(0 \leq v \leq 1\). What is the value of \(N^2\)?

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