Yea, this is a good illustration. For example, for an intersection of two planes going through origin, the plane equation coefficients are (a multiple of) the

Yea, this is a good illustration. For example, for an intersection of two planes going through origin, the plane equation coefficients are (a multiple of) the of the normal vector coefficients. Now, the intersection vector must be perpendicular to both planes normals, so if you take the cross product of the two vectors, you get the intersection vector. This in this case I would just look at it and instantly do a cross product of the coefficients, whereas you would eventually do precisely the same, but reasoning algebraically, perhaps just as fast. In this case, thinking algebraically doesn't seem to yield the intimate relationship with your object of study required for creativity, just because of the geometric nature of it. But this reasoning wouldn't be much use in -- for instance -- fiddling with discrete mathematics, where you may get more intimate precisely by reasoning algebraically!