What is right-handed coordinate system? In the determinant section, I can't understand what is the right-handed coordinate system.
TEXTBOOK says a coordinate system {$u,v$}is called right-handed if $u$ can be rotated in a counterclockwise direction throught an angle $\theta (0 < \theta < \pi)$.
But what on earth that talking about? What's that meaning in here?
I know it is related to a area and volume, but once I can't follow the notion "right-handed"
I can't understand what determinant do at all!
 A: A right-hand coordinate system is modelled by, wait for it, the right hand! Hold out your right hand in a fist with the thumb facing up. Stick up your thumb like your giving a thumbs up. Now extend the index finger, like your pointing at something in from of you. Finally, extend the middle finger side ways so that it's at a right-angle with the thumb and the index finger. The index finger is in the direction of the positive $x$-axis, the middle finger in the direction of the positive $y$-axis and the thumb the positive $z$-axis. If you're in two-dimensions, chop off your thumb! (Please don't.)

A: Just look at your favorite $xy$ coordinate system on paper. If you rotate the positive $x$-axis by $\frac \pi2$ (or $90^\circ$) counterclockwise, it lands on the positive $y$-axis. That makes this coordinate system a right-hnded one.
If you swap the roles of $x$ and $y$ however, the chirality is changed: You would have to rotate the $y$-axis by $-\frac\pi2$ to bring it to the $x$-axis. Therefore, the $yx$-coordinate system is left-handed.
