From 70308e2285b3e043df68132c3e75196795ead4ee Mon Sep 17 00:00:00 2001 From: Alvie Rahman Date: Thu, 26 May 2022 22:40:01 +0100 Subject: [PATCH] add volume of parallelapiped --- uni/mmme/1026_maths_for_engineering/vectors.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/uni/mmme/1026_maths_for_engineering/vectors.md b/uni/mmme/1026_maths_for_engineering/vectors.md index a9a71fe..941bd0e 100755 --- a/uni/mmme/1026_maths_for_engineering/vectors.md +++ b/uni/mmme/1026_maths_for_engineering/vectors.md @@ -121,7 +121,7 @@ vector such that the three vectors from a right handed system: This is technically not a determinant because not all the elements are numbers but shhhhhh... -### Scalar Triple Product +### Scalar Triple Product (and co-planar vectors) \begin{align*} [ \pmb a, \pmb b, \pmb c ] &= \pmb a \cdot (\pmb b \times \pmb c) \\ @@ -211,6 +211,10 @@ $$\cos\theta = \frac{\pmb a \cdot \pmb b}{|\pmb a||\pmb b|} = \frac{a_1b_1 + a_2 $$area = |\pmb a||\pmb b|\sin\theta = |\pmb a \times \pmb b|$$ +### Volume of a Parallelepiped + +$$volume = | [ \pmb a, \pmb, b, \pmb c ] |$$ + ### Equation of a Straight Line A straight line can be specified by