Right hand rule proof

[fk378]

Can anyone explain how to use the right hand rule to determine whether a vector will be "into the page" or "out of the page"?

 

[Defennder]

See:
http://en.wikipedia.org/wiki/Right_hand_rule

 

[HallsofIvy]

It would help to know what vector you are talking about!

The "right hand rule" appears in relation to the cross product of vectors, magnetic fields, etc. What, exactly is your problem?

 

[fk378]

Here is a problem:

Find |u x v| and determine whether u x v is directed into the page or out of the page.

|u| = 5 and is directed in the direction of the z-axis.
|v| = 10 and and is 60 degrees clockwise from the vector u.

 

[Defennder]

60 degrees clockwise in which plane?

 

[fk378]

They are in the same plane.

 

[Redbelly98]

Here is a problem:

Find |u x v| and determine whether u x v is directed into the page or out of the page.

|u| = 5 and is directed in the direction of the z-axis.
|v| = 10 and and is 60 degrees clockwise from the vector u.

I'm assuming u and v are in the plane of the page.

With your right hand, make a "backwards L", with the 4 fingers lined up together and your thumb pointing off to the side.

Point the 4 fingers in the direction of u (the first vector in the cross product).

Keeping those fingers pointing along u, rotate or twist your hand so that the palm faces clockwise (i.e., towards the direction of v, the 2nd vector in the product).

Your thumb is now pointing in the direction of u x v.

 

[Defennder]

Is the z-axis lying in the plane of the page? If so, then by this picture:

http://en.wikipedia.org/wiki/Image:Rechte-hand-regel.jpg

Let your thumb be 'u', your forefinger be 'v'. Your middle finger is now pointing in the direction of u x v.