In response to the 3D Intersections and PView Function posts Lori Miller has sent me two very elegant alternative ways of achieving similar results.

The first is an on-spreadsheet solution to the intersection of two lines, using the LinEst function:

Intersection point of two 3D lines

Note that if the lines intersect, Point 1 and Point 2 will have the same coordinates, otherwise they will be different.

The second is a perspective projection of a hypercube (specifically a 4D hypercube, or tesseract):

Tesseract Perspective Projection

 It took me some time to work out how this one worked.  The file is an xlsx, so there is no VBA, but also there is no visible data (other than a single number associated with each of the slider bars), but no hidden rows, columns or sheets either.  The secret is that all the data and calculations are in array formulas in defined names.  Have a look in the name manager and see if you can work out the algorithm.

The files may be downloaded from:

LineIP.xlsx

Hypercube.xlsx