"intersection of interest" is correct and usable in written English.
You can use it to refer to a situation in which two or more people or groups might have something in common. For example, "Their paths crossed at the intersection of interest and they soon became close friends."
Saddam Hussein's invasion of Kuwait, in August , 1990 provided a rare intersection of interests between Washington and Damascus.
I believe there is a certain degree of intersection of interests between bureaucrats and political leaders.
Continued research at this intersection of interests will hopefully shed more light on both biases and fallacies.
The summit will turn a blind eye to Iran's strikes in Iraq because this is an "intersection of interests" between Iran and the Gulf countries taking part in the anti-ISIS coalition led by the United States.
If there is an intersection of interests between Israel and Sunni Arab states, it will pivot around their shared hostility towards Iran, Hezbollah and the Shiite crescent, including the Popular Mobilization Forces in Iraq and the Houthis in Yemen.
The street canyon intersection is of interest as it provides the basic case study to demonstrate most of the factors that will apply in a wide range of urban situations.
For Jeremy Yoder, a postdoctoral fellow in the Department of Forest and Conservation Sciences at the University of British Columbia, Vancouver, his metascience research about LGBTQA (lesbian, gay, bisexual, trans*, queer, or asexual) scientists' experiences was "the intersection of personal interest and serendipity," he says.
One of the points where there is a significant, long-lasting intersection of the interests of many philosophers with the interests of many people of all kinds and conditions concerns the nature and significance of death.
"Milk" understands that modern politics thrive at the messy, sometimes glorious intersection of grubby interests and noble ideals.
All have stumbled into a complex intersection of government interests after the attacks of Sept. 11, 2001, as a crackdown to protect national security collides with a long tradition of protecting juveniles.
As someone cited by both analytic philosophers and postmodernists, Wittgenstein embodies the intersection of their interests, or at least that possibility.
