In Genesis 28:20, 'he vowed a vow' means that there was a desire that what is wished for may come about, thus that the Lord may provide it. Within a vow, something of a bargain is present, and at the same time on man's part, something of a bounden duty to keep his side of it, should he obtain his desire.

(Odkazy: Arcana Coelestia 3732)

'Vanity' signifies evil and the falsity of evil. 'Vanities of strangers' signify falsities of religion.

In Exodus 5:9, vain words signify truths when said by people who believe falsities. (Arcana Coelestia 7122)

(Odkazy: Apocalypse Explained 340)