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Yes, "Vart ska du?" is correct since "vart" indicates a direction and "ska" can be used to mean "go".
"Var ska du?" is an incomplete sentence since "var" indicates position. You would have to add another word to make the sentence complete.
For example, you could say "Var ska du sova" - Where will you sleep?
In words like 'bort', adding an 'a' or other similar changes at the end signifies being at rest, while keeping the word unchanged means there is movement.
For example, 'Jag ska gå hem' means 'I will go home' (movement), while 'Jag är hemma' means 'I am at home ' (stationary)
'Hon gick långt bort' means 'She went far away' (movement), and 'Hon är långt borta' means 'She is far away' (stationary)
Hope this helped!