You Do Need power plug adapter while traveling from Balearic Islands to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Balearic Islands are C and F. This is how they look like.

Balearic Islands

In Balearic Islands, outlets of type C and F are in use.

Type C

Type F

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K