What is the origin of transaction I have a bitcoin-qt wallet on computer A and some of the private keys are stored on another computer B with the ability to send transaction as well. I have to following questions :   


If I generate the transaction on B and send it to bitcoin network
will it show up on the bitcoin-qt transaction history computer A ?
If 1 is true, Just by looking on computer A can I know which computer
generated the tx ?
If I generate the transaction on B and send it to bitcoin network will it show up on the bitcoin-qt transaction history on computer A?


Yes, when you make transactions, your transactions are broadcast to other nodes, and then the entire network. Your node will surely have the transaction in memory pool / blockchain, as long as your Bitcoin Core is fully synced. But it'll only appear on the history tab if at least one of the inputs of the transaction was held in a private key that computer A has.


  If question one is true, just by looking on computer A can I know which computer generated the tx?


There's no way understand if you're using Bitcoin Qt (I don't know if there's a full node client that does that) - it doesn't log if it created the transaction, or it received the transaction from a node.

You can use web clients, for example GreenAddress. They log when you logged in with your IP address and time. Then you can try to find which computer it is by inspecting its IP address and date and time.