Confirmation for Simplifying Vector Product: Can Constants be Taken Out?

[fishspawned]

this is a general question - the thing I'm working on if what i am asking makes sense - i am currently only looking for a confirmation on what i think is right

this is a vector product question:

if i have:

(A/c x cB)

can i look at that as:

(1/c*c)(A x B)

which comes to

A x B

the question is - can i take the constant, c, out in the way i am showing? i ask this as i cannot find an identity that confirms this.

 

[Andrew Mason]

this is a general question - the thing I'm working on if what i am asking makes sense - i am currently only looking for a confirmation on what i think is right

this is a vector product question:

if i have:

(A/c x cB)

can i look at that as:

(1/c*c)(A x B)

which comes to

A x B

the question is - can i take the constant, c, out in the way i am showing? i ask this as i cannot find an identity that confirms this.

Just use the definition of cross product of two vectors X and Y, which is a vector which has magnitude |X||Y|sinθ in a direction given by the right hand rule perpendicular to the plane of X and Y. What are the magnitudes of $1/c(\vec{A})$ and $c\vec{B}$?

AM

 

[wisvuze]

A/c X cB by definition is the vector such that
< A/c X cB, n > = Det [ A/c , cB, n ] for all n. By the properties of the determinant,
Det [ A/c , cB, n ] = 1/c*c Det[A,B,n] = Det[A,B,n] = < A X B, n > for all n. Finally,
< A/c X cB, n > - < A X B, n > = 0 for all n, so A X B = A/c X cB.( < > is the inner product, or just the dot product in this case )