What is the Angle Between Vectors Method?

[learningphysics]

-1 to 1.....

Exactly.

So using that same idea, when is \theta well defined in the dot product formula?

 

[t_n_p]

-1 to 1...LOL

 

[learningphysics]

-1 to 1...LOL

But what has to be between -1 and 1, for \theta to be defined?

It was x in that formula I gave... but in the dot product formula it is...?

 

[t_n_p]

for theta to be defined, http://img356.imageshack.us/img356/5728/untitledjq2kn7.jpg has to be between -1 and 1

 

[learningphysics]

for theta to be defined, http://img356.imageshack.us/img356/5728/untitledjq2kn7.jpg has to be between -1 and 1

Exactly. So that's what you need to prove, to show that \theta is well defined... you need to show that that expression is between -1 and 1 for any two 4-vectors v and w.

It's a tough problem if you're solving from scratch... There a theorem called the "Cauchy-Schwarz inequality" that shows that this is true almost immediately... Have you covered it in your course?

 

[t_n_p]

Havn't learned the theorem. If it's essenetial to the question, I don't know why they ask non relevant questions...

 

[learningphysics]

Havn't learned the theorem. If it's essenetial to the question, I don't know why they ask non relevant questions...

Hmmm... it might also be called by another name...

Basically the Cauchy-Schwarz inequality says

|\overrightarrow{v}.\overrightarrow{w}| \le |\overrightarrow{v}||\overrightarrow{w}|

and from that the result you want follows immediately...

you've probably got something like that explained or proven in your text. Look it up in your text or online...

did your tutor say anything else about this problem?

 

[learningphysics]

I'll catch you later t_n_p. I got to :zzz:

 

[t_n_p]

Never seen anything remotely like that before! My tutor just said try best, don't worry too much if I can't do it.

 

[t_n_p]

I'll catch you later t_n_p. I got to :zzz:

no worries, thanks alot!