Doesn't "vet" translate to "know"? How is "känner" different as compared to "vet"?
"Att veta" is more about knowing facts while "att känna" is used when talking about people you are friends or acquainted with (and "att känna" also means "to feel"). :)
I like comparing 'vet' and 'känner' to the french 'savoir' et 'conaître' respectively. Regularly french has better translations for swedish words than english does. Another example is 'hos' matching with 'chez' better than anything in english.
ömsesidig(-t/-a) – but if you use it like in our mutual friend, that is vår gemensamma vän.