From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 5 Feb 2019 23:24:10 +0000 (+1100)
Subject: collinearity
X-Git-Tag: yr12~260
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/4668fb43d1433ec7fae2ac4828f4affced12971c?ds=inline

collinearity
---

diff --git a/spec/vectors.md b/spec/vectors.md
index 0b6ea2a..db65983 100644
--- a/spec/vectors.md
+++ b/spec/vectors.md
@@ -139,6 +139,8 @@ Vector resolute of $\boldsymbol{a}$ in direction of $\boldsymbol{b}$ is magnitud
 
 $$\boldsymbol{u}={{\boldsymbol{a}\cdot\boldsymbol{b}}\over |\boldsymbol{b}|^2}\boldsymbol{b}=\left({\boldsymbol{a}\cdot{\boldsymbol{b} \over |\boldsymbol{b}|}}\right)\left({\boldsymbol{b} \over |\boldsymbol{b}|}\right)=(\boldsymbol{a} \cdot \hat{\boldsymbol{b}})\hat{\boldsymbol{b}}$$
 
+Scalar resolute of $\vec{a}$ on $\vec{b} = |\vec{u}| = \vec{a} \cdot \hat{\vec{b}}$
+
 ## Vector proofs
 
 **Concurrent lines -** $\ge$ 3 lines intersect at a single point  
@@ -175,3 +177,6 @@ $$\cos \alpha = {a_1 \over |\vec{a}|}, \quad \cos \beta = {a_2 \over |\vec{a}|},
 
 **on CAS:** `angle([a b c], [1 0 0])` for angle between $a\vec{i} + b\vec{j} + c\vec{k}$ and $x$-axis
 
+## Collinearity
+
+Points $A, B, C$ are collinear iff $\vec{AC}=m\vec{AB} \text{ where } m \ne 0$