From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 25 Jun 2019 04:52:58 +0000 (+1000)
Subject: [spec] start vector functions
X-Git-Tag: yr12~101
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/5727605c4011fe198b16d530c572c71212945457?ds=sidebyside

[spec] start vector functions
---

diff --git a/spec/vectors.md b/spec/vectors.md
index 932f614..3a940e3 100644
--- a/spec/vectors.md
+++ b/spec/vectors.md
@@ -185,3 +185,11 @@ i![](graphics/vectors-3d.png)
 Parametric equation of line through point $(x_0, y_0, z_0)$ and parallel to $a\boldsymbol{i} + b\boldsymbol{j} + c\boldsymbol{k}$ is:
 
 \begin{equation}\begin{cases}x = x_o + a \cdot t \\ y = y_0 + b \cdot t \\ z = z_0 + c \cdot t\end{cases}\end{equation}
+
+## Vector functions
+
+$$\boldsymbol{r}(t)=x\boldsymbol{i}+y\boldsymbol{y}$$
+
+- If $\boldsymbol{r}(t)$ represents position with time, then the graph of endpoints of $\boldsymbol{r}(t)$ represents the Cartesian path.
+- Domain of $\boldsymbol{r}(t)$ is the range of $x(t)$
+- Range of $\boldsymbol{r}(t)$ is the range of $y(t)$