Apache RewriteEngine is not working with virtual host setup - mod-rewrite

Question

I have a basic virtual host setup enabled on my machine, and it works fine when I just type in the server name. However, when I include "RewriteEngine On" it kills it. Yes, I do have the rewrite module installed, and yes, I have restarted apache. I'm not actually attempting any rewrite rules yet, because just the act of turning the thing on is enough to make it stop working. Any clue as to what's going on? Seems like if the module is included, this ought to work. What am I forgetting? Here's what I've got in my virtual host file
NameVirtualHost *:80
<VirtualHost *:80>
ServerAdmin webmaster#localhost
DocumentRoot "C:/www/mysite/public/"
ServerName mysite
RewriteEngine on
<Directory "C:/www/mysite/public/"
Options Indexes FollowSymLinks
AllowOverride all
Order Deny,Allow
Allow from all
</Directory>
</VirtualHost>
When I remove the "RewriteEngine on" line, everything works. When I put it back in, it breaks. I could understand if I had some weird rule in there, but simply turning it on shouldn't break anything.

Answer 1

Perhaps mod_rewrite isn't enabled in your setup? You can try to put the RewriteEngine On line inside an test like so
<IfModule mod_rewrite.c>
RewriteEngine On
</IfModule>

Answer 2

I assume you an Ubuntu-like system.
Go to /etc/apache2/sites-available/your_site.conf
Open your_site.conf using your favorite text editor.
Add/Update the Directory section as below
<Directory /var/www/>
Options Indexes FollowSymLinks
AllowOverride All
Require all granted
</Directory>
Save it and restart apache.