Word meanings!!
vyavasāy : resolute; determined
ātmikā : for the purpose of
buddhih : intelligence
Cited by Śrīla Prabhupāda at
https://vaniquotes.org/wiki/BG_02.41_vyavasayatmika_buddhir…_cited
vyavasāyātmikā buddhiḥ, or the absolute path of perfection
https://vanisource.org/wiki/SB_2.4.3-4?hl=vyavasāyātmikā%20buddhiḥ
The resolute purpose of a person in Kṛṣṇa consciousness is based on knowledge. Vāsudevaḥ sarvam iti sa mahātmā su-durlabhaḥ: a person in Kṛṣṇa consciousness is the rare good soul who knows perfectly that Vāsudeva, or Kṛṣṇa, is the root of all manifested causes. As by watering the root of a tree one automatically distributes water to the leaves and branches, so by acting in Kṛṣṇa consciousness one can render the highest service to everyone—namely self, family, society, country, humanity, etc. If Kṛṣṇa is satisfied by one’s actions, then everyone will be satisfied.
Service in Kṛṣṇa consciousness is, however, best practiced under the able guidance of a spiritual master who is a bona fide representative of Kṛṣṇa, who knows the nature of the student and who can guide him to act in Kṛṣṇa consciousness. As such, to be well versed in Kṛṣṇa consciousness one has to act firmly and obey the representative of Kṛṣṇa, and one should accept the instruction of the bona fide spiritual master as one’s mission in life.
The consciousness of the soul becomes polluted by the material atmosphere, and thus various activities are exhibited in the false ego of bodily identification. These various activities are described in Bhagavad-gītā (2.41) as bahu-śākhā hy anantāś ca buddhayo 'vyavasāyinām. The conditioned soul is bewildered into various activities for want of pure consciousness. In pure consciousness the activity is one. The consciousness of the individual soul becomes one with the supreme consciousness when there is complete synthesis between the two.
https://vanisource.org/wiki/SB_3.6.7?hl=bahu-śākhā%20hy%20anantāś%20ca|buddhayo%20'vyavasāyinām
As stated in Bhagavad-gītā (2.41), devotional service to the Lord is one, and the mind of the devotee is not diverted to the many branches of uncertainties. Vidura’s purpose was to be situated in that service to the Lord, wherein one merges undivertedly.
https://vanisource.org/wiki/SB_3.7.40?hl=the%20mind%20of%20the%20devotee%20is%20not%20diverted
Śrīla Viśvanātha Cakravartī Ṭhākura describes in his explanation of the verse in Bhagavad-gītā, vyavasāyātmikā buddhiḥ, that one who wants to be certain to achieve spiritual success must take the instruction from the spiritual master as to what his particular function is. He should faithfully try to execute that particular instruction and should consider that his life and soul. The faithful execution of the instruction which he receives from the spiritual master is the only duty of a disciple, and that will bring him perfection. One should be very careful to receive the message from the spiritual master through the ears and execute it faithfully. That will make one’s life successful.
https://vanisource.org/wiki/SB_3.22.7?hl=vyavasāyātmikā%20buddhiḥ
When one becomes serious to follow the mission of the spiritual master, his resolution is tantamount to seeing the Supreme Personality of Godhead. As explained before, this means meeting the Supreme Personality of Godhead in the instruction of the spiritual master. This is technically called vāṇī-sevā. Śrīla Viśvanātha Cakravartī Ṭhākura states in his Bhagavad-gītā commentary on the verse vyavasāyātmikā buddhir ekeha kuru-nandana (BG 2.41) that one should serve the words of the spiritual master. The disciple must stick to whatever the spiritual master orders. Simply by following on that line, one sees the Supreme Personality of Godhead.
https://vanisource.org/wiki/SB_4.28.51?hl=vyavasāyātmikā%20buddhir|ekeha%20kuru-nandana
This material world is often described as an ocean of nescience. In such an ocean, everything is agitated. The mind of a great devotee is also like an ocean or a very large lake, but there is no agitation. As stated in Bhagavad-gītā (2.41): vyavasāyātmikā buddhir ekeha kuru-nandana. Those who are fixed in the service of the Lord are not agitated by anything.
https://vanisource.org/wiki/SB_4.24.20?hl=vyavasāyātmikā%20buddhir|ekeha%20kuru-nandana
“Those who are on the spiritual path are resolute in purpose, and their aim is one. O beloved child of the Kurus, the intelligence of those who are irresolute is many-branched.”
When a devotee is advancing toward spiritual realization, his only aim is the service of the Supreme Personality of Godhead. He does not care for any other material or spiritual activity. King Purañjana represents the ordinary living entity, and the woman represents the ordinary living entity’s intelligence. Combined, the living entity enjoys his material senses, and the intelligence supplies all paraphernalia for his enjoyment. As soon as he enters the human form, the living entity is entrapped by a family tradition, nationality, customs, etc. These are all supplied by the māyā of the Supreme Personality of Godhead. Thus the living entity, under the bodily conception of life, utilizes his intelligence to his best capacity in order to satisfy his senses.
Actually, those who are in knowledge of everything are determined to execute Kṛṣṇa consciousness, but those who are rascals (mūḍhāḥ), sinners (duṣkṛtinaḥ) and the lowest of mankind (narādhamāḥ), who are bereft of all intelligence (māyayāpahṛta jñānāḥ) and who take shelter of the demoniac way of life (āsuraṁ bhāvam āśritāḥ), are disinterested in Kṛṣṇa consciousness. As such they become implicated and take on so many activities. Most of these activities center around the killing of animals. Modern civilization is centered around animal-killing. Karmīs are advertising that without eating meat, their vitamin value or vitality will be reduced; so to keep oneself fit to work hard, one must eat meat, and to digest meat, one must drink liquor, and to keep the balance of drinking wine and eating meat, one must have sufficient sexual intercourse to keep fit to work very hard like an ass.
Unfortunately, living beings under the influence of material nature ask for many other things, and they are described in the Bhagavad-gītā (2.41) as having divided, or splayed, intelligence. Spiritual intelligence is one, but mundane intelligence is diverse. In Śrīmad-Bhāgavatam (7.5.30-31) it is stated that those who are captivated by the temporary beauties of the external energy forget the real aim of life, which is to go back to Godhead. Forgetting this, one tries to adjust things by various plans and programs, but this is like chewing what has already been chewed. Nonetheless, the Lord is so kind that He allows the forgetful living entity to continue in this way without interference.
https://vanisource.org/wiki/ISO_8
Devotee: Verse 41. “Those who are on this path are resolute in purpose and their aim is one. O beloved child of the Kurus, the intelligence of those who are irresolute is many-branched. Men of small knowledge are very much attached to the flowery words of the Vedas which recommend various fruitive activities for elevation to the heavenly planets, resultant good birth, power and so forth. Being desirous of sense gratification and opulent life, they say that there is nothing wrong in this (Bg. 2.41-3).”
Prabhupāda: In the Vedas there are many allurements for elevating oneself to higher standard of life. Just like in this life also the father says, “My dear boy, if you become highly educated, then you’ll get a very nice job, you’ll get good salary, and you’ll have nice apartment, and nice wife, children.” Just like these are allurements for enticing one in this materialistic way of life, similarly there are many allurements in the Vedic literatures. People are also, I mean to say, allured to execute such thing, that if you make such and such pious activities, then you get elevated to such and such higher planets and you get such and such high standard of life. These are explained there. But Kṛṣṇa says that don’t be misled by these allurements.