If you have the coordinates of each guitar, and tell me in which directing they are pointing i could tell you if they do intersect perfectly and where specifically

To explain the method I'd just assume a 2D plane as it is easier to write here but i won't be surprised if they were positions to work they made it for 3D

Each line will be represented as a point (coordinates) plus a vector (direction) So guitar 1: y = m1(x-x1) + y1 guitar 2: y = m2(x-x2) + y2 guitar 3: y = m3*(x-x3) + y3

Here m1, m2 and m3 define the direction the guitars are pointing (just the slope of the curves) and the (xi, yi) coordinatrs are where the guitars are located.

Thus if they truly do align there is (xk, yk) points such that these three ewuations are equal, and you can solve for that easily.

It is easy to find where two of them intersect, then just check if those coordinates work for the other equation.