THE BEST WAY TO CHANGE THE BF3 DIRECTORY:
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I just spent an hour making illustrated instructions, but I do not yet have enough reputation to use images in posts. However, the method below is correct for changing the directory. 

### STEP 1
Go to:  `C:/Program Files (x86)/Origin` and copy the Origin file

###STEP 2
Paste the copied file onto the drive of your choice. If the drive is blank you'll need to create a new file extension. [Click on this text to learn how][1].  
I’ll use F Drive for the example. `F:/Program Files (x86)`

*Note:  These big files can take some time, depending on your drive speed, to Paste onto the new drive. Mine took 18 minutes transfer the files but it beats countless hours of internet download! :-)

###STEP 3
Now follow the same procedure to Copy and Paste the, "**Origin Games**" file into "**Program Files ( x86)**", in the new drive (F: Drive in this example) exactly as before.

###STEP 4
Now you need to open Origin and change the default directory location by doing the following: 

 - Open Origin
 - Click on the Origin Tab (top left)
 - Now click on “Application Settings” and in the sub category click on “Advanced”. on the right you’ll see,  "your games will be downloaded here". Click "Change..". 
 - Since we already created the correct folder and subfolders, just click in the text box, and go to the Drive letter and change it from the old drive (example `C:\Program Files (x86)\Origin Games\`) to the new drive (example `F:\Program Files (x86)\Origin Games\`)

###STEP 5 (Now comes the fun part!)
Close Origin and go to "Add or Remove Programs" and uninstall BF3. Open Origin back up, go to "My Games" drag your mouse over Battlefield 3, and chose download.
Amazingly enough it should take a total of 3 to 10 seconds for the entire operation. If it’s taking too long then close Origin and restart the download. Again it should be done almost instantly!

  [1]: http://www.ehow.com/how_8163849_make-subfolder.html