The phrase "exist at the intersection of" is correct and commonly used in written English.
It's generally used to refer to a point in which multiple elements or concepts overlap or come together. For example, "My research exists at the intersection of engineering, mathematics, and physics."
All the more when we exist at the intersection of socially marginalised groups.
Those of us who exist at the intersection of marginalized sexuality and race now have a storied tradition of fighting for space in the world.
Mr. Zuckerberg, in his reference to Intel, rightly said of his own company: "We exist at the intersection of technology and social issues".
Much like a one-man Jam & Lewis or Gamble & Huff, his productions exist at the intersection of hip-hop, house and R&B, reclaiming the sounds of the 80s and 90s and repackaging them for 2016.
The ubiquity and power of information technology means that the biggest security risks exist at the intersection of disciplines and communities.
Virtual, augmented and mixed experiences that exist at the intersection of our physical and digital worlds will bring the humanity of the face-to-face conversation back into the evolution of our communication.
There is a real desire to experiment with the form in the UK — and a real acknowledgment that biography exists at the intersection of many arts and sciences.
The program exists at the intersection of several recent reality themes — obsessive behavior, hoarding, thrift — all delivered with the punch of a game show.
East meeting West, North meeting South: since time immemorial, the Wakhan Valley, in the Pamir Mountains, has existed at the intersection of trails trodden by nomads, peddlers, pilgrims and, at times, the soldiers and emissaries of great powers.
