VirtualHost configuration issue - apache

Question

I have two apps I want to serve via port 80 in Apache on the same ip host. To do so, I have defined the following virtual hosts:
NameVirtualHost *:80
<VirtualHost *:80>
DocumentRoot "/var/www/wsgi/rest_api"
ServerName api
WSGIDaemonProcess rest_api user=gms threads=5
WSGIScriptAlias /api /var/www/wsgi/rest_api/rest_api.wsgi
WSGIPassAuthorization On
<Directory /var/www/wsgi/rest_api/rest_api>
Order deny,allow
Allow from all
Options +Indexes
</Directory>
</VirtualHost>
<VirtualHost *:80>
DocumentRoot "/var/www/extjs/cardiocatalogqt"
ServerName cardiocatalogqt
Alias /cardiocatalogqt /var/www/extjs/cardiocatalogqt
<Directory /var/www/extjs/cardiocatalogqt>
Options Indexes FollowSymLinks
AllowOverride None
Order Deny,Allow
Allow from all
</Directory>
</VirtualHost>
The problem is that only the first one in the list is being recognized (they both work independently). What am I missing to get both of these working together, independent of order?
EDIT
I am trying to avoid use of different server names due to a CORS authentication issue across domains (which includes host names and ports). All I want is two different paths as such to resolve accordingly: http://test.com/cardiocatalogqt and http://test.com/api.

Answer 1

Please create two different virtual host with different server names and different document root paths
<VirtualHost *:80>
ServerAdmin admin#test.com
ServerName test.com
ServerAlias www.test.com
DocumentRoot /var/www/test.com/public_html
ErrorLog ${APACHE_LOG_DIR}/error.log
CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>
Also, add the server name into the hosts file.

Answer 2

mod_alias was what I wanted, ala http://httpd.apache.org/docs/2.2/mod/mod_alias.html
Works like a charm!
EDIT
More specifically, my config looks like this:
WSGIDaemonProcess rest_api user=gms threads=5
WSGIScriptAlias /api /var/www/wsgi/rest_api/rest_api.wsgi
WSGIPassAuthorization On
<Directory /var/www/wsgi/rest_api/rest_api>
Order deny,allow
Allow from all
Options +Indexes
</Directory>
<VirtualHost *:80>
DocumentRoot "/var/www/extjs/cardiocatalogqt"
ServerName cardiocatalogqt
Alias /cardiocatalogqt /var/www/extjs/cardiocatalogqt
<Directory /var/www/extjs/cardiocatalogqt>
Options Indexes FollowSymLinks
AllowOverride None
Order Deny,Allow
Allow from all
</Directory>
</VirtualHost>