Does anyone know the source for the following quote?
Destiny determines the consequences of our actions but not the actions themselves.
I heard that this is told by Vidura to Dhritarastra. This article also claims the same.
There is a popular conversation between Vidura and Dhritarashtra. It is called Vidura Neeti or Vidura Geeta which extends for nine chapters i.e., chapter 33 to 41 of the Udyoga Parva of the Mahabharata.
The exact quote is not present in the Vidura Neeti but a verse which implies the same i.e., destiny is stronger than one's actions or will is present. This is not said by Vidura. It is Dhritarashtra who said that.
From Section 40 of Udyoga Parva (Translated by Kisari Mohan Ganguli)
Although, however, I incline in my mind towards the Pandavas even as thou teachest me to do, yet as soon as I come in contact with Duryodhana it turneth off in a different way. No creature is able to avert fate. Indeed, Destiny, I think, is certain to take its course; individual exertion is futile.
He says that as a response to Vidura's discourse to declare Yudhistira as the king and treat Pandavas equal with his own sons.