TITLE: How do you find the sine of the angle between two vectors?
QUESTION [5 upvotes]: I do not know what the sine of the angle between two vectors is. I think it may be the vector created by connecting the tips of the two vectors but I am not sure. 
How do you find the sine of the angle between two vectors?

REPLY [7 votes]: In general for $\mathbf{a},\mathbf{b}\in\mathbb{R}^3$, we have
$$\|\mathbf{a}\times \mathbf{b}\|=\|\mathbf{a}\|\|\mathbf{b}\|\sin\theta,$$
where $\theta$ is the angle between $\mathbf{a}$ and $\mathbf{b}$.