TITLE: Is the cross product of two unit vectors itself a unit vector?
QUESTION [26 upvotes]: Or, in general, what does the magnitude of the cross product mean? How would you prove or disprove this?

REPLY [7 votes]: $|\vec{a}\times\vec{b}|=|\vec{a}||\vec{b}||\sin(\theta)|$
Let $a,b$ unit vectors, so we have $|a| = |b| = 1$
$|\vec{a}\times\vec{b}|=|\sin(\theta)| \le 1$ (equality is when $|\sin(\theta)| = 1$ i.e. when a and b are perpendicular)
Therefore in general the result won't be a unit vector.