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The best way to achieve that is using Vue Router.
But, if you want to do that without routing you should do it with Dynamic Components
<component is=""></component>
You can see an example here: https://jsfiddle.net/lucaskatayama/256Lo0xa/1/
There is an App, with a button to toggle a component inside <component></component>.
It simulates your switch, by changing the selected component.
Source:stackexchange.com