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

1. Sep 7, 2011

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!

2. Sep 7, 2011

micromass

Staff Emeritus
Try to calculate this norms with the inner product:

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

3. Sep 7, 2011

Fjolvar

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

4. Sep 7, 2011

micromass

Staff Emeritus
What did you get when you wrote it out:

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

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

???

5. Sep 7, 2011

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.

6. Sep 7, 2011

Fjolvar

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

7. Sep 7, 2011

micromass

Staff Emeritus
What is yor notation for the dot product then??

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