I'm currently teaching myself a lot of math while working through a book on maths and physics for game programmers. I've had to start from scratch and currently have worked through from linear algebra, trig and now vectors. I'm afraid the book that I have skirts over a lot of detail, which I'm not happy with, so I often have to trawl the Internet for further explanation.
I've hit on a problem that I can't find the answer for so hopefully someone on this forum could point me in the right direction?
So, I'm going through the chapter on vectors and looking at using algebra with vectors to calculate where 2 lines intersect. There a four position vectors (a,b,c,d) of the four points A, B, C, D. These are drawn in a figure, where a line from A to B crosses over a line from C to D. The book lists two linear simultaneous equations for solving the problem:
1. t(b1 - a1) + s(c1 - d1) = c1 - a1
2. t(b2 - a2) + s(c2 - d2) = c2 - a2
For the life of me, I can't solve these equations. I don't have to, but I'd like to as I want to know why it works.
Can anyone help me get started, I can solve t for equation 1 and then substitute t in equation 2 to try and solve s, but then I'm stuck!
Thanks in advance for anyone who can help.