How to update testcase using OSLC api

 The URL you are using is an OSLC query, not the URL of a resource. PUT would not be possible on a query URL.

I suspect that you were being redirected to the login page because you did not authenticate to the server properly. It appears that you tried to do Basic Authentication during the PUT, which is not possible when most servers are using Form Based Authentication (by default).

To authenticate, you need to POST to /qm/authenticated/j_security_check. See the comment section in the OSLC Workshop and another article for sample codes.
https://jazz.net/library/article/635
https://jazz.net/library/article/633

As Jim mentioned, you have to PUT to a resource URI, not a query URL, for the update. For more details, see the document.
https://jazz.net/wiki/bin/view/Main/RqmOslcQmV2Api#HTTP_PUT_POST_Requests

Note that the URL for partial update looks a bit like a query URL, but it is not, as the first part of it is still a proper resource URI. For example:
https://clm.jkebanking.net:9443/qm/oslc_qm/contexts/_8aqdofQkEeex1tX1crJPcQ/resources/com.ibm.rqm.planning.VersionedTestCase/_pfYp8fQlEeex1tX1crJPcQ?oslc.properties=dcterms:title