Was Sage Agastya the guru of Sage Vaśiṣṭha?

 

Shri Bhagavata Purana 6.18.6 contains a on the birth of Sages Agastya and Vaśiṣṭha

Upon seeing Urvaśī, the celestial society girl, both Mitra and Varuṇa discharged semen, which they preserved in an earthen pot. The two sons Agastya and Vasiṣṭha later appeared from that pot, and they are therefore the common sons of Mitra and Varuṇa.

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However, Rig Veda mentions Agastya to be much senior to Vaśiṣṭha, and if understood correctly, Agastya was the Guru of Vaśiṣṭha.

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Rig Veda 7.33.11 says that Sage Vaśiṣṭha is the son of Mitra and Varuna. It also states that Sage Vaśiṣṭha was the mind-born son of Urvaśī or Sarasvatī.

If understood properly, Mitra and Varuna are the divinities, but not physical goods. The statement that Sage Vaśiṣṭha was mind-born son of Urvaśī should be understood as Sage Vaśiṣṭha getting SELF REALISATION/BLISS, with the blessing of Urvaśī or Sarasvatī.

Rig Veda 7.33.10 says that after Sage Vaśiṣṭha attaining SELF REALISATION or spiritual re-birth, Sage Agastya brought him to the people/beings - tat te janmotaikaṃ vasiṣṭhāgastyo yat tvā viśa ājabhāra.

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So, if inferred strictly based on the Rig Veda without considering later date Bhagavata Puranic contexts, we can understand that Sage Agastya might be guiding Sage Vaśiṣṭha in spiritual practices, and thus, Sage Agastya should be considered as the guru of Sage Vaśiṣṭha.