I seek help to solve a geometry problem related to constructing magnetic sense coils.I freely admit that in this company I must be a relative klutz at math, but I do not mind working to the solution myself. What I need is a few pointers to a viable strategy.
Three identical rectangular planes placed together so the short sides are touching along their length, all to form an isoceles triangle. (This structure would be similar to a taller form of the triangular jig used to set up snooker balls before a game commences!)
Each plane contains a line through its centre, parallel to the long sides. These lines are the 'zero datum' for an angle we want to find. Now if these lines were all equally rotated about the rectangle centres by some angle (it is less than 90 degrees!), and keeping within their respective planes, there comes a stage where the lines are all mutually perpendicular.
I seek an approach to find that angle. All the ways I have tried so far lead me into a hopeless jungle of trig algebra that falters on human failings. I have thought to exploit the vector cross product
A X B = 0 ~ ~ as a test for perpendicularity. The vector approach seemed quite attractive....at first.
I have tried a different scheme by placing the lines on the faces of a cube. This guarantees perpendicularity, and we have at least the centres located, but the triangular set of planes is then tipped into trigonometric mire.
This is the kind of thing where some kid can spot a trick condition that solves it easy...maybe. It has proven quite awkward for me.