# Right Hand rule, explain please?

[SOLVED] Right Hand rule, explain please?

I don't have a problem, I just have issues with understanding the right-hand rule, if someone could explain it (with pictures if possible) I would appreciate it, although it might be better in person because I could see the motion.

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Hootenanny
Staff Emeritus
Gold Member
Consider the following diagram,

The right-hand rule is defined such that it conforms to the right-hand coordinate system. In the right-handed coordinate system with the usual unit vectors (i, j, k) the cross product between i and j gives, by definition, k,

i X j = k

Which simply means that if one rotates the x-axis counter-clockwise by $\pi/2$ such that it lies collinear with the y-axis, then the result is the z-axis. The right-hand rule is commonly used to determine the direction of a cross product, especially in physics problems.

Consider the cross product describe above (iXj), which basically means rotating the vector i (the x-axis) toward the vector j (y-axis). Now, take your right-hand and keeping your thumb straight (as if giving the 'thumbs up') curl your fingers in the direction which the x-axis is rotating (in this case toward the y-axis). Your thumb should now be pointing straight upwards, in the direction of k (the z-axis).

Now consider the following cross product,

j X i

Using the same method as above try to curl your fingers in the direction of rotation (i.e. from the y-axis to the x-axis), you'll probably find that you'll have to turn your hand upside down. If you have done it correctly, your thumb should be pointing direction downwards (towards the negative z-axis). Hence, you have used the right hand rule to determine the cross product,

j X i = -k

Indeed, it is very difficult to describe the right-hand rule without demonstrating it. However, I hope you've found my post useful.

It was, very useful, I had never had it explained to me like that, which makes more sense seeing the diagram, thanks!

Hootenanny
Staff Emeritus