Vector relationship? |A+B| = |A-B|

[Fjolvar]

I've been spending far too much time on this problem and I know I'm over thinking it. Here it is:

If |A+B| = |A-B|

What is the most general relationship between the two vectors?

-Now I know this is just saying they have equal magnitude regardless of direction, but I'm not quite sure what it's asking for. What kind of general relationship am I supposed to write out? Any help would be greatly appreciated. Thanks!

 

[micromass]

Try to calculate this norms with the inner product:

$$|A|^2=<A,A>$$

 

[Fjolvar]

Try to calculate this norms with the inner product:

$$|A|^2=<A,A>$$

I'm still not seeing how to relate vector A and B using this.. =/

 

[micromass]

What did you get when you wrote it out:

$$|A+B|^2=<A+B,A+B>=...$$

$$|A-B|^2=...$$

?

 

[dillingertaco]

$<A+B,A+B>=<A-B,A-B>$
By properties of the dot product..
$<A,A>+2<B,A>+<B,B>=<A,A>-2<B,A>+<B,B>$

Get everything to one side and deduce from that.

 

[Fjolvar]

We haven't learned this notation yet unfortunately. Is this the only possible approach?

 

[micromass]

We haven't learned this notation yet unfortunately. Is this the only possible approach?

What is yor notation for the dot product then??