I am developing a petitions site that is using RESTFul techniques.

For example: /petition/1 indentifies a certain petiton (resource).

How should I name 

a) Signing a petition?

/petition/sign/1
or
/petition/1/sign
or
???

b) Searching for a petition based on terms (rich, for example)

/petition/search/rich
/petition?search=rich

And lastly

c) Seeing only a certain category

/petition/category/1
/petition?category=1

Thank you.