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 $$N^2$$?

×