Question: I want to create a page similar to trello in javascript using vue.js
What can I use to make such sliding frames - arrays with tasks inside?
it is about an element that can be grabbed with a mouse and moved to another place

Answer: 
Trello board is an implementation of a `Kanban board`. So while searching in Google, that should be your keyword.

<https://github.com/BrockReece/vue-kanban> e.g. is what you are looking for.
Found this example for your concern : <https://vuejsexamples.com/a-realtime-kanban-board-in-vue-js-and-hamoni-sync/>. It seems to be quite what you need to begin with...