From 0c024e93b606406843aad28e1e3948e956241e91 Mon Sep 17 00:00:00 2001
From: Preston Pan <preston@nullring.xyz>
Date: Sun, 25 Dec 2022 16:54:59 -0800
Subject: change webring

---
 .../linear_algebra/source/introduction.ms           |  16 +++++++++++++++-
 .../linear_algebra/source/introduction.pdf          | Bin 24790 -> 25350 bytes
 2 files changed, 15 insertions(+), 1 deletion(-)

(limited to 'website/mathematics/linear_algebra')

diff --git a/website/mathematics/linear_algebra/source/introduction.ms b/website/mathematics/linear_algebra/source/introduction.ms
index 106ffec..6b69a41 100644
--- a/website/mathematics/linear_algebra/source/introduction.ms
+++ b/website/mathematics/linear_algebra/source/introduction.ms
@@ -45,7 +45,8 @@ coord x 0, 11 y 0, 11
 Now, let's imagine that this point $(3, 2)$ represents a force in a certain direction.
 For example, we can draw a line from the origin to this point and the resulting force's
 magnitude will be represented by the length of the line in question (which can be obtained
-via the pythagorean theorem).
+via the pythagorean theorem), and the direction of the force will be outwards from the origin
+following the line.
 
 .G1
 draw solid
@@ -55,3 +56,16 @@ coord x 0, 11 y 0, 11
 "(3, 2)" above at 3,2
 "$sqrt {3 sup 2 + 2 sup 2}$" above at 1,2
 .G2
+
+.PP
+We can now imagine another line segment drawn from the origin $(-1, 3)$, which we can imagine
+to be another force acting in a different direction with a different magnitude:
+
+.G1
+draw solid
+coord x -10, 10 y -10, 10
+0 0
+3 2
+-1 3
+"(3, 2)" above at 3,2
+.G2
diff --git a/website/mathematics/linear_algebra/source/introduction.pdf b/website/mathematics/linear_algebra/source/introduction.pdf
index b74d28a..563569a 100644
Binary files a/website/mathematics/linear_algebra/source/introduction.pdf and b/website/mathematics/linear_algebra/source/introduction.pdf differ
-- 
cgit