Non-Zero Vectors A, B parallel iff. AxB=BxA (true/false)

[Hansel13]

This is a true/false question. I said it was false, and I was wrong. I still don't know how it's true.

Statement:
Non zero vectors A and B are parallel if and only if A x B = B x A.

Could someone tell me how this is True?

Thanks.

 

[galactus]

Re: Vectors

The vectors are parallel if their normals are parallel. The cross products are the same if the normals are scalar multiples of one another.

\(\displaystyle A\times{B}=0\) iff A and B are parallel.

Take for instance, \(\displaystyle A=(3,-4,5)\) and \(\displaystyle B=(-6,8,-10)\)

In this case, \(\displaystyle A\times{B}=B\times{A}\)

 

[Hansel13]

Re: Vectors

The vectors are parallel if their normals are parallel. The cross products are the same if the normals are scalar multiples of one another.

Take for instance, \(\displaystyle A=(3,-4,5)\) and \(\displaystyle B=(-6,8,-10)\)

In this case, \(\displaystyle A\times{B}=B\times{A}\)

Ahhh, thank you. That makes a lot of sense.