From cb4fb3e05fb3470e50a6ede102078aa5c00ffcf9 Mon Sep 17 00:00:00 2001 From: eggy Date: Thu, 3 Jun 2021 21:18:02 -0400 Subject: [PATCH] math: Add plane intersections --- docs/mcv4u7.md | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/docs/mcv4u7.md b/docs/mcv4u7.md index 178d577..e069b16 100644 --- a/docs/mcv4u7.md +++ b/docs/mcv4u7.md @@ -602,6 +602,19 @@ $$d=\frac{|Ax_1+By_1+Cz_1+D|}{\sqrt{A^2+B^2+C^2}}$$ The shortest distance between two parallel planes is equal to: $$d=\frac{|D_1-D_2|}{\sqrt{A^2+B^2+C^2}}$$ +Two planes are parallel if their direction vectors are scalar multiples of each other: +$$\vec n_1 = k\vec n_2$$ + +If they are also coincident, the D-values will also be identical: +$$D_1=D_2$$ + +Otherwise, the planes intersect, the line along which is equal to the cross product between the two direction vectors. +$$\vec m=\vec n_1\times\vec n_2$$ + +An initial point vector can be solved by setting any of the variables ($x,y,z$) to zero and solving for the others. Alternatively, the parameter $t$ can be set equal to one of the variables instead and the parametric equation derived that way. + +The **angle between two planes** is equal to the angle between their normal direction vectors, which can be determined using the dot product formula. + ## Resources - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)