I came across an interesting problem in the MathsJam Shout for February 2022.
(“MathsJam is a monthly opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like. Puzzles, games, problems, or just anything they think is cool or interesting. Monthly MathsJam nights happen in over 70 locations around the world, on the second-to-last Tuesday of each month. To find your nearest MathsJam, visit the website at www.mathsjam.com.”)
“Given two lines Ax + By + C = 0 and ax + by + c = 0, is there a simple link between the vectors (A, B, C), (a, b, c), and the point where the lines cross?”
The answer, of course, is yes, but the question is somewhat open-ended and I was not able to track down any answer given.
See the Point of Intersection Problem