Originally Posted by

**mathDad** The angle between vectors $\displaystyle \mathbf{u}$ and $\displaystyle \mathbf{v}$ is defined as follows.

$\displaystyle \cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\left|\left| \mathbf{u} \right|\right| \left|\left| \mathbf{v} \right|\right|}$

It's derivation is straightforward.

The angle between two planes is equal to the angle between the planes' normal vectors, $\displaystyle \mathbf{n}_1$ and $\displaystyle \mathbf{n}_2$. But then the book says the angle between the two planes is

$\displaystyle \cos \theta = \frac{\left| \mathbf{n}_1 \cdot \mathbf{n}_2 \right|}{\left|\left| \mathbf{n}_1 \right|\right| \left|\left| \mathbf{n}_2 \right|\right|}$

I assume the absolute value in the numerator is a because we want to take the acute angle between the two lines. Is that right? If not, why is it there? How does the absolute value represent the acute angle?