Vectors: Components and the Position Vector

In this video I show how we can treat vectors algebraically by introducing a coordinate system and the concept of a position vector. Since vectors are considered equivalent if they have the same magnitude and direction, then they can be placed anywhere in a coordinate system and still be equivalent. However, if we move that vector such that its tail starts from the origin, then we can consider the coordinates of it's arrow head as the "components" of that vector; which we can represent using triangle brackets and call the "position vector". We can calculate the position vector from any vector that is offset away from the origin by subtracting each of the x, y, and z components from each other from the tail to arrow head coordinates. I also illustrate this concept with an example at the end of the video.

The timestamps of key parts of the video are listed below:

- Components: 0:00
- Equivalent Vectors: 3:00
- Position Vector: 7:09
- Equation 1: 13:10
- Example 3: 13:44

This video was taken from my earlier video listed below:

- Vectors and the Geometry of Space: Vectors: https://youtu.be/0lJiVlKw4Kc
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EiRECLVkBCcFhSpbSz8XIw

Related videos:

Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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