cross product of time-domain vector functions is not necessarily zero

[PG1995]

Hi

Could you please help me with this query? Thank you.

Regards
PG

 

[MrAl]

Hi,

What are you trying to do there? A and B are defined already so just cross them. They contain x and y components so you end up with a z component.

I get this (x,y,z unit vectors):
0*x+0*y+(-sin(t*w)^2-cos(t*w)^2)*z

so there is only a z component left which reduces to:
-1*z

or just:
-z

Maybe you should try using the cross product more directly.

 

[PG1995]

Thank you, MrAl.

I'm also left with z component at the end but my answer doesn't match with the given one. I was just being more detailed. I have been trying to figure out why my answer doesn't match with the given one without any success. If you could trace that mistake it would be really kind. Otherwise, it's okay. Thanks.

Regards
PG

 

[steveB]

PG,

What is the purpose of this mathematics? It seems odd to me that you care about complex vectors of this type. What is the physical meaning of these complex vectors in a 3D space?

 

[dougy83]

No, they're not equivalent.

You are missing a minus sign in the third line from the bottom of your working.

Also, if you use the form they've given you, i.e. A(t)xB(t) = z[-cos^2(wt)-sin^2(wt)], you can use a single trig identity (cos^2(x) + sin^2(x) = 1) to arrive at A(t)xB(t)=-z

 

[PG1995]

Thank you, Doug.

Yes, it should have been minus sign instead of plus one.

PG,

What is the purpose of this mathematics? It seems odd to me that you care about complex vectors of this type. What is the physical meaning of these complex vectors in a 3D space?

The purpose is learning and nothing else! It's a course about electromagnetic theory and the book has a chapter on complex vectors. The book is quite confusing. As for the the physical meaning in 3D space, I would say that good things come to those who wait patiently and keep working! I don't yet know their actual significance. But I'm sure it will become handy soon. Some years ago math was the subject I hated the most and prime reason I had to justify my hatred was that it had no practical use! Thank you for always being there to help me.

Best wishes
PG

 

[steveB]

The purpose is learning and nothing else! It's a course about electromagnetic theory and the book has a chapter on complex vectors. The book is quite confusing. As for the the physical meaning in 3D space, I would say that good things come to those who wait patiently and keep working! I don't yet know their actual significance. But I'm sure it will become handy soon.

Thank you for explaining! Knowing it is for EM theory places the material in better context for me to understand your questions and try to help. Indeed, it will be useful for EM theory and applications.

I was worried that this was being studied in the context of phasor theory which you are also discussing recently. This seemed to be the wrong context and that it would just lead to more confusion on that subject.

I'll just caution you to keep in mind that there are vast differences between 3D vectors with complex values and complex numbers which are often treated as 2D vectors in the complex plane.