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Did Vivekananda say "If the mind is intensely eager..."?
Not in his works
No. "If the mind is intensely eager, everything can be accomplished, mountains can be crumbled into atoms." does not appear in Swami Vivekananda's Complete Works. Searched vols 1 to 8 with a fuzzy match, and Wikisource (all volumes, including vol 9) by phrase. No passage comes close.
The version people share
“If the mind is intensely eager, everything can be accomplished, mountains can be crumbled into atoms.”
Seen on: AZQuotes.
Lines he did say
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Is "If the mind is intensely eager..." in the Complete Works of Swami Vivekananda?
No. We searched volumes 1 to 8 with a fuzzy match and Wikisource across all nine volumes by phrase. Nothing comes close.
How do you check a Vivekananda quote?
Search a distinctive phrase in the Complete Works (Advaita Ashrama, nine volumes; the text is on ramakrishnavivekananda.info and Wikisource). If only quote sites carry it, with no volume or lecture named, treat it as unverified.
Sources and method
Matched against The Complete Works of Swami Vivekananda, Mayavati Memorial Edition, vols 1 to 8 (9,239 paragraphs, Bengali translations checked separately), with Python difflib. In his words: 90 or more out of 100. Paraphrase: 70 to 90. Not in his works: under 70, and no hit in a phrase search of Wikisource across all volumes, including vol 9. This line scored 55.