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As we know from the Brahmasutra (composed by Badarayana Rishi), the Bhagavad Gita and the Upanishads show us the source of Mukti(emancipation) and this way is Nivrtiya(निवर्तीय), whereas the way described in Veda are प्रवृत्ती (prvartiya).

So my question is, what is difference between the Nivrtiya(निवर्तीय) way and the प्रवृत्ती (prvartiya) way?

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The four classical goals of life (purusharthas) are dharma, artha, kama and moksha. Pravritti is the path of action where one aims for dharma, artha and kama and lives a prosperous and a pleasant life. Nivritti is renunciation of artha and kama as one's goal in life.

Gita 16.7 says: The demoniac do not know about the way of action (pravritti) or the way of renunciation (nivritti). Neither purity, nor good conduct, nor truth is found in them.

Basically pravritti is the path of pious householders while nivritti is the path of monks.

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Pravruti means indulgence in material activities and nivruti means non-indulgence in them.

Vedas have two primary portions, Karma Kanda and Jnana Kanda. The Karma kanda portion of the Vedas lead out the path of pravruti and the Jnana Kanda part of the Vedas (to which the Upanishads belong) lead out the path of nivruti.

In the path of pravruti, one can obtain heaven and higher planets by properly following the scriptural injunctions and the varnashrama dharma. But in the path of nivruti, the sole objective is attainment of the formless Brahman, there is no desire for personal enjoyment or worldly emotions.

The Vedas contain pravruti way because it is better to follow scriptural injunctions and prohibitions and go to heaven than to lead an unregulated barbaric life and fall to hell. So the Bhagavatam explains:

phalaśrutiriyaṃ nṝṇāṃ na śreyo rocanaṃ param
śreyovivakṣayā proktaṃ yathā bhaiṣajyarocanam
[SB - 11.21.23]

Meaning
Those statements of scripture promising fruitive rewards do not prescribe the ultimate good for men but are merely enticements for executing beneficial religious duties, like promises of candy spoken to induce a child to take beneficial medicine.

And because the path of nivruti doesn't award the asscoication with the Lord, in Bhagavatam Shri Krishna says to give up both pravruti and nivruit, both scriptural injunctions and prohibitions, and practice only His devotion:

tasmāt tvam uddhavotsṛjya codanāṁ praticodanām
pravṛttiṁ ca nivṛttiṁ ca śrotavyaṁ śrutam eva ca
mām ekam eva śaraṇam
[SB - 11.12.14,15]

Meaning
Therefore, My dear Uddhava, abandon the Vedic mantras as well as the procedures of supplementary Vedic literatures and their positive and negative injunctions. Disregard that which has been heard and that which is to be heard. Simply take shelter of Me alone.

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