# Length of vector resulting from cross product

I have the following question. In physics forces are vectors. Now I may write a force as $$$$\mathbf{F} = F \mathbf{e}_F$$$$ with $$F$$ denoting the length and $$\mathbf{e}_F$$ denoting the direction vector. But some forces are the result of a cross product (pseudo vectors). The length is then $$$$\vert\mathbf{a}\vert \vert\mathbf{b}\vert \sin(\theta)$$$$ with $$\mathbf{a}, \mathbf{b}$$ some vectors (maybe position and velocity) and $$\theta$$ the angle between them. However these vectors are also sometimes written in the first form. How can I check whether $$F$$ in the first form is the length of a cross product, or not?

You can always choose $$|a|, |b|, \theta$$, that will give you that vector so... ...$$F$$ is always a length of infinite cross products. What are the restrictions? You must pick $$a, b$$ in a plane orthogonal to $$F$$!
• In the other formula, you can change the sign of $e_F$ by putting a minus before it or you can put a minus directly before $F$. This will change their direction. Jun 6, 2019 at 15:53
• ...or you can swap $|b|$ with $|a|$. Jun 7, 2019 at 0:51