In a parallelogram how do I determine angle and area of vectors?

Question

Consider the vectors

$\vec{u}$ = (1, 0) and $\vec{v}$ = (0, 1)

1. Determine cosθ, where θ is the angle between $\vec{u}$ and $\vec{v}$.
2. Determine the area of the parallelogram determined by $\vec{u}$ and $\vec{v}$.

Now, I have my answers as follow:

1. 0 (since the cosine of 90 degrees is 0)
2. Area = base * height = 1 * 1 = 1

I'm not sure if this is correct though. Any assistance will be greatly appreciated.

Answer 1

I guess my answer was correct in the first place.

1. 0 (since the cosine of 90 degrees is 0)
2. Area = base * height = 1 * 1 = 1