- #1
Doc Al said:Note that [tex]\hat{R}[/tex] is a unit vector that is perpendicular to [tex]\vec{d\ell}[/tex].
The magnitude of any cross product is given bygsan said:yes, I'm understand that dl is perpendicular to unit vector of R, but how the magnitude of them become dl only?
Doc Al said:The magnitude of any cross product is given by
[tex]\vec{A}\times\vec{B} = AB\sin\theta[/tex]
Applying this to your question, B is a unit vector and theta = 90, so
[tex]AB\sin\theta = A[/tex]
Make sense?
What aspect do you not understand? A = dl; B = 1; theta = 90.gsan said:I not really understand about the 2nd formula, could explain more?
Doc Al said:What aspect do you not understand? A = dl; B = 1; theta = 90.
Have you worked with vector cross products before?
It represents the magnitude of the unit vector [tex]\hat{R}[/tex], which is 1.gsan said:why the B=1 ?
Doc Al said:It represents the magnitude of the unit vector [tex]\hat{R}[/tex], which is 1.
Perhaps you are confusing [tex]\vec{R}[/tex], which has magnitude of R, with [tex]\hat{R}[/tex], which has magnitude of 1?
It's a unit vector! The purpose of a unit vector is to define a direction; unit vectors--by definition--have magnitude of 1.gsan said:how do u know the [tex]\hat{R}[/tex] has magnitude of 1 ?
Why not? A unit vector is a perfectly good vector, just like any other.gsan said:now my another question is, why we can cross product of a vector with a unit vector?
Doc Al said:True. But realize that here you need the cross product of vector dl and unit vector R hat, not vector R. The magnitude of R hat must equal 1.
Given your definition of vector R, what would be unit vector R hat? (Hint: Find the magnitude of vector R.)
Assuming that the vector dl is purely in the x direction (for some reason), then version 1 is correct. Version 2 treats dl as a unit vector, which it is not.gsan said:and now my question is
the cross product of vector of dl and vector of R should be
|hat{x} hat{y} hat{z}|
| dl 0 0 |
| 3 2 3 |
or
|hat{x} hat{y} hat{z}|
| 1 0 0 |
| 3 2 3 |
which 1 should be correct? 1st or the 2nd?
Doc Al said:Assuming that the vector dl is purely in the x direction (for some reason), then version 1 is correct. Version 2 treats dl as a unit vector, which it is not.
In general, dl will be in some arbitrary direction.
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