Is it permissible to slaughter a calf vowed to Allah Almighty and designated for the poor, on the occasion of a son's marriage and to feed the poor from it?

This vow is considered a conditional vow designated for the poor, so it is not permissible to spend it on others. It is not valid to make it a feast from which others eat, nor is it permissible for the one who made the vow to eat from it.