From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 16 Oct 2018 23:38:26 +0000 (+1100)
Subject: vectors - 20c
X-Git-Tag: yr11~21
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/0ae966a7d8bc3a8d3d9ee64b0b67df55a002fe51

vectors - 20c
---

diff --git a/spec/vectors.md b/spec/vectors.md
index 5c6df9c..86bd95b 100644
--- a/spec/vectors.md
+++ b/spec/vectors.md
@@ -73,3 +73,27 @@ A vector of length 1. $\vec{i}$ and $\vec{j}$ are unit vectors.
 
 A unit vector in direction of $\vec{a}$ is denoted by $\hat{\vec{a}}$
 
+Also, unit vector of $\vec{a}$ can be defined by $\vec{a} \cdot {|\vec{a}|}$
+
+## Scalar products / dot products
+
+If $\vec{a} = a_i \vec{i} + a_2 \vec{j}$ and $\vec{b} = b_i \vec{i} + b_2 \vec{j}$, the dot product is:
+$$\vec{a} \cdot \vec{b} = a_1 b_1 + a_2 b_2$$
+
+Produces a real number, not a vector.
+
+$$\vec{a} \cdot \vec{a} = |\vec{a}|^2$$
+
+## Geometric scalar products
+
+$$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta$$
+
+where $0 \le \theta \le \pi$
+
+## Perpendicular vectors
+
+If $\vec{a} \cdot \vec{b} = 0$, then $\vec{a} \perp \vec{b}$ (since $\cos 90 = 0$)
+
+## Finding angle between vectors
+
+$$\cos \theta = {{\vec{a} \cdot \vec{b}} \over {|\vec{a}| |\vec{b}|}} = {{a_1 b_1 + a_2 b_2} \over {|\vec{a}| |\vec{b}|}}$$