Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 3.1 Column Vector

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Vertex Model of Triangle

Let's use column vectors to create a vertex model of a triangle in two dimensions. We define our three vertices as follows:

\begin{aligned} {\vec{v}}_{1} = [\begin{array}{c} 0 \\ 0 \end{array}], & {\vec{v}}_{2} = [\begin{array}{c} - 1 \\ 1 \end{array}], & {\vec{v}}_{3} = [\begin{array}{c} 2 \\ 1 \end{array}] . \end{aligned}

Remark. In this model, we assume each vector represents a point in a two-dimensional space. The entry in the first row of each vertex vector encodes distance along the horizontal axis. The entry in the second row encodes distance along the vertical axis.
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Remark. When we graph these vertices, we do not connect the dots because this model does not encode links between vertices.

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Excalidraw Data

Text Elements

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WITH external force
Spring Mass Chain at equilibrium
with NO external force (t=0 sec)

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Embedded Files

3b1137dc3488130f0426281066cc4cdb86150ca1: $x_{1}$
28393dfb5fbbb11062a64a5349b3d2ad74216c6b: $x_{1} (t)$
b4c673079ee8391431f52a861441e23c282935ea: $x_{2}$
b37230525c3687593a13ef4286596359b835cb6a: $m_{1}$
67adcbf0e450fd865247abdf223b5fdbbfb6b193: $m_{2}$
30ce668f797c9c1a4864fecddd89d649f36e9bbe: $x_{2} (t)$
4220b76d93da23ed409042a358e0ba65cb445c12: $m_{1}$
bd3e400664b2f1c56c5dd7b6a03ec869ffd8a086: $m_{2}$
dbbee70a8808cc8d9dafe49327e52eaacb658d63: $u_{1} (t)$
49e1fa22f8b8a6dd52e6b8fa147915a9b6ce3144: $u_{2} (t)$
eb390ed816872c4ee1e1a3cab7b6270bc7c313f8: [[Pasted Image 20240404224753_081.png]]

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