You shouldn't be giving names to your <option> tags. The <select> they belong to is what you should be looking at.
<select name="search_where">
<option value="web"> web </option>
<option value="images"> Images </option>
<option value="videos"> Videos </option>
</select>
Then in your code, you can check the value thusly:
switch ($_GET['search_where']) {
case 'web':
include 'search_web.php'; // execute search_web.php
break;
case 'images':
include 'search_images.php'; // execute search_images.php
break;
case 'video':
include 'search_video.php'; // execute search_video.php
break;
default:
die('invalid search criteria');
}
EDIT: had to change $_GET key to match form.
That would allow you to execute different php scripts depending on what was selected, however, you still have a pretty big chore to search other sites.