If $U \times V$ is a unit vector, $|U| = \sqrt{3}/3, |V| = 2$ and $U\cdot V > 0$, then what is the angle between $U$ and $V$?

Question

If $U \times V$ is a unit vector, $|U| = \sqrt{3}/3$, $|V| = 2$ and $U \cdot V > 0$, then what is the angle between $U$ and $V$?

Is this just dot product? $U \cdot V = |U| |V| \cos(\theta)$? Solve for $\theta$?

Answer 1

Hint 1: We have $|U\times V|=|U| |V|\sin\theta$ where $\theta$ is the angle between $U$ and $V$. For example, see here. Now you know $|U\times V|$, $|U|$ and $|V|$, and you can solve for $\theta$.

Hint 2: On the other hand, by the formula you have, i.e. $U \cdot V = |U| |V| \cos(\theta)$, we also know that $\cos\theta>0$.