What principle was established in the school-sponsored prayer case of Engel v. Vitale?

The principle established in Engel v. Vitale (1962) was that the government, including public schools, cannot sponsor or endorse religious activities, including voluntary school-sponsored prayer. The Supreme Court ruled that even a non-denominational, voluntary prayer intended to promote moral values violated the Establishment Clause of the First Amendment. This case set a precedent for the separation of church and state in educational settings, emphasizing that public institutions should remain neutral on matters of religion.