Daṇḍa means "a long rod," and vat means "like." Before a superior, one has to fall down on the ground just like a stick, and this sort of offering of respect is called daṇḍavat. Atri Ṛṣi offered his respect to the three deities in that way. They were identified by their different carriers and different symbolic representations. In that connection it is stated here that Lord Viṣṇu was sitting on Garuḍa, a big aquiline bird, and was carrying in His hand a disc, Brahmā was sitting on a swan and had in his hand kuśa grass, and Lord Śiva was sitting on a bull and carrying in his hand a small drum called a ḍamaru. Atri Ṛṣi recognized them by their symbolic representations and different carriers, and thus he offered them prayers and respects.
(Srimad Bhagavatam----4:1:24----purport).

Lord Brahmā bowed down like a stick, and because Lord Brahmā's complexion is golden, he appeared to be like a golden stick lying down before Lord Kṛṣṇa. When one falls down before a superior just like a stick, one's offering of obeisances is called daṇḍavat. Daṇḍa means "stick," and vat means "like." It is not that one should simply say, "daṇḍavat." Rather, one must fall down. Thus Brahmā fell down, touching his foreheads to the lotus feet of Kṛṣṇa, and his crying in ecstasy is to be regarded as an abhiṣeka bathing ceremony of Kṛṣṇa's lotus feet.
(Srimad Bhagavatam----10:13:62----purport).

The word daṇḍa means "rod," and vat means "like." To offer obeisances to the spiritual master, one must fall flat exactly as a rod falls on the ground. This is the meaning of the word daṇḍavat.
(Sri Caitanya Caritamrta----2:24:271----purport).