Question

What arrangements of axes follow the "right-handed coordinate system"?

Answer 1

you can solve this systematically

Answer 2

the right hand rule gives us 3 possible setups for the axes, and the left hand rule gives us 3 possible setups , for a total of 6 possible setups
(there are 6 ways to order x,y,z if you think about it 3! )

Answer 3

If you don't mind doing some contortions with your hand:-)

"If the index finger of the right hand is pointed forward, the middle finger bent inward at a right angle to it, and the thumb placed at a right angle to both, the three fingers indicate the relative directions of the x-, y-, and z-axes in a right-handed system. The thumb indicates the x-axis, the index finger the y-axis and the middle finger the z-axis."

Answer 4

I do not understand the difference between the right and left hand coordinate system (how it works). I understand that you use your thumb/index/middle finger to determine the positives axes (x,y,z). Which finger stands for which axes?

Answer 5

right, there are three ways you can contort your right hand such that x is your right first finger , y is your middle right hand finger, and z is your thumb

Answer 6

well , without loss of generality, suppose you designate the x axis as your first finger, the y axis as your middle finger, and the z as your thumb. do this for right hand and left hand

Answer 7

there is no way to contort your right hand so that it fits a left hand coordinate system

Answer 8

Oh! So it doesn't matter which finger is which axes as long as you move your fingers around and keep the respected fingers/axes?

Answer 9

hmmm, well in my example i set the first finger as x, middle as y, and z as thumb. but you can move your hand around