I have been throwing around hand gestures for the past hour in a feeble attempt at trying to solve this question involving a cross product of two vectors $a$ x $b$. So far, I haven't found any satisfactory explanation on the internet as to how this rule is supposed to help me find out whether the components of $a$ and $b$ are positive, negative or zero. E.g., James Stewart explains it as though it is obvious (it isn't):
If the fingers of your right hand curl through the angle $\theta$ from $a$ to $b$, then your thumb points in the direction of $n$
What does he mean by "curl"? Sorry if this is a dumb question but I am getting really frustrated trying to use this "rule" to solve what is seemingly a really elementary question. I imagine it would be more intuitive if someone could just "show" me how to do it, but since that is not possible, if anyone could offer an explanation that is more helpful than the above, I would appreciate it.
(This question is specifically in reference to Exercise #4, Chapter 9.4 in Stewart's Single-variable calculus book, 4th edition.)
The figure shows a vector a in the xy-plane and a vector $b$ in the direction of $k$. Their lengths are $||a|| = 3$ and $||b|| = 2$. a) find $||a$ x $b||$ b) Use the right-hand rule to decide whether the components of a x b are positive, negative or zero
I am stuck on part b).