[Vuejs]-Vue Js Login Components

some suggestions:

1. Having separate pages for each flow would be better, one for the login, one for the recover password, one for the register, etc, because you can share the exact URL to the user (will be easier with vue router)
2. If the flow is very small, you can have a parent component that handles the main flow and several children components for each flow (forms), you can use Vue dynamic component https://v2.vuejs.org/v2/guide/components.html#Dynamic-Components
3. You need to think about how are you going to handle the authentication (json web tokes/ simple password, oauth2), that will be a really important thing before doing the functionality.