Final answer:
Samson is the judge who helped deliver the Israelites from the Philistines and broke a Nazirite vow by allowing his hair to be cut.
Step-by-step explanation:
The judge who delivers the Israelites from the Philistines but breaks a Nazirite vow is Samson. The story of Samson is found in the Book of Judges in the Hebrew Bible. Samson was granted extraordinary strength by God to aid him against his enemies and perform heroic feats such as slaying a lion with his bare hands and defeating an entire army with only the jawbone of a donkey. His Nazirite vow, a promise made to be consecrated to God, included abstentions from cutting his hair, consuming alcohol, and touching the dead. However, Samson broke his vow when he fell in love with Delilah, who betrayed him to the Philistines. They cut his hair while he was asleep, which was the source of his strength, and he was captured. In the end though, when his hair began to grow back, he called upon God one last time and demolished a Philistine temple, killing himself and many Philistines in the process.