Your geometric explication is what I have assumed to be the case; nonetheless, thanks for the taking the time to spell everything out in detail - very much appreciated.
But here's my question.
For x1 on (x2,x3), Excel reports two slopes, which I assume to be the slopes of your two lines in the (x1,x2) and (x1,x3) planes.
Excel also reports a single intercept, which I assume to be the intercept of your plane on the x1 axis.
And if this assumption is correct, isn't it also the case that the two lines (in the (x1,x2) and (x1,x3) planes) intersect at this intercept (given the fact that these two lines define the plane with this intercept)?