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If you prefer a more intuitive way of looking at it I would say that when you have two vectors of the basis, i and j, then a right-hand system means that the third vector of the basis will be pointing in the direction of the thumb of your right hand when you point the rest of your fingers in the i direction and bend them towards the j direction.
Think of the natural way your right hand would move when you want to slap someone. That's also the way fingers of your right hand curl. Sorry if this is a dumb answer. – Shitikanth. Apr 14, 2012 at 5:14. The RHR is supposed to help you visualize the result of a cross product.
7. 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 way I remembered the rule for how magnetic fields around wires work is the following. Take your right hand, and point your thumb in such a way so that it points in the same direction as the current, and curl the rest of your fingers. The direction your fingers curl represents the direction of the magnetic field.
1. Say I'm taking the cross product of vectors a a and b b. Say that b b is totally in the z z direction and has length 7 7, so b = 7k b = 7 k. Say that a a is in the xy x y -plane with positive coefficients, a = 3x + 4y a = 3 x + 4 y. I want to understand the sign of the components of a × b a × b using the right hand rule.
$\begingroup$ I haven't done a lot of math in a while so I might be wrong but I think it was counterclockwise.Draw a right hand coord. sys on a piece of paper - x points to the right and y to the upper border of the sheet.Add to that a circle with the center of the coord system also being its center.Write down some angles - 0, 45, 90 etc.Your z will be "sticking" out of the plane towards you ...
Hold out your right hand and point your index finger at the screen, your middle finger (horizontally) to the left, and your thumb vertically. You have a right-handed coordinate system. Do the same with your left hand, and you'll notice that the middle fingers point in different directions. Hold your right hand and left hand out in front of you ...
4. There are several equivalent definitions, but here is one that is often convenient: The ordered triplet (→A, →B, →C) of vectors in R3 is right called right-handed if det (→A, →B, →C)> 0, where (→A, →B, →C) is the square matrix formed by taking the three vectors as columns. (Note that the determinant is necessarily nonzero ...
The convention is to use the right-hand rule: Point the fingers of your right hand along A and curl them in the direction of the small angle (i.e., the angle less than π) toward B. If your right thumb makes an acute angle with C, the ordered triple {A, B, C} is said to be right-handed. (Otherwise the ordered triple {A, B, C} is left-handed.)
The right hand rule is a common convention for describing orientation of coordinates, used throughout physics. It's also used in the definition of the cross product. Is it possible to give a purely mathematical definition of the right hand rule, which doesn't reference anyone's hand? What is unique about the right hand that the RHR captures?