Talk:Line-plane intersection

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  • The calculations assume that the line and plane intersect at a point. This is not always the case (they might not intersect, or they might intersect identically; the line might be a subset of the plane). These cases should also be covered.
  • Add additional material from this version: [1].

My recollection of matrix mathematics is a little hazy, but the bit I added:

\begin{bmatrix} x_a - x_0 \\ y_a - y_0 \\ z_a - z_0 \end{bmatrix} = \begin{bmatrix} x_a - x_b & x_1 - x_0 & x_2 - x_0 \\ y_a - y_b & y_1 - y_0 & y_2 - y_0 \\ z_a - z_b & z_1 - z_0 & z_2 - z_0 \end{bmatrix} \begin{bmatrix} t \\ u \\ v \end{bmatrix}

...should be correct. ~~ jim d

Also, I'd be more comfortable seeing the vectors referred to in AB, BC -style notation, eg. : J − A = tJK + uAB + vAC or perhaps something like P_J - P_A = t \times V_{JK} + u \times V_{AB} + v \times V_{AC} which is more sane in the algebraic sense than the former. Can someone who routinely uses these kind of formulae please make a call? ~~ jim d

[edit] no sense whatsoever

I have not taken calculus or any higher maths, but the variables don't seem to be labeled. Most people, specifically me, have no idea what p is, so to say that p = X1 and Y1 means nothing. LFStokols 01:23, 9 March 2007 (UTC)LFStokols

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