This is my first post here, so hello all.
I'm not sure whether this counts as 'advanced geometry', but here goes.
Between two 3D objects (assume they are spherical), there lies a tangent plane. I need to find any one vector that falls on the tangent plane, other than [0,0,0].
This is for a 3D application, so the time taken to run any calculations used is important. I need to find an arbitrary vector perpendicular to the (known) normal between two points, and parallel with the tangent plane; that is probably a better description than a vector that falls on the tangent plane.
In 2D, this can be done by swapping the components of the known normal, and multiplying one of them by -1.. Is there a similar 'quick' method for 3D?
I am more of a programmer than a mathemetician; and most information I have found uses terminology I don't fully understand. I'd prefer an explanation of a suitable method that I can understand rather than an answer.
Thanks for reading.