Name: Standard Basis Vectors i, j, k
Uploaded: 2023-04-30T18:10:41+00:00
Duration: 18 min 54 s
Description: In this video I introduce standard basis vectors which are special vectors with a length 1 and point in the direction of the x, y, and z axis, and are labeled i, j, and k, respectively. Any vector can

1 year ago

vectors standard basis vectors vector algebra vector analysis mathematics science math stem education math easy mes

In this video I introduce standard basis vectors which are special vectors with a length 1 and point in the direction of the x, y, and z axis, and are labeled i, j, and k, respectively. Any vector can be written as a summation of scalar multiples with the standard basis vectors. This concept helps in describing and visualizing vectors. Later in the video I go over a historical note on vectors and the concept of "quaternions" which have both a scalar and a vector component. However, the concept of quaternions has been largely displaced by modern forms of vector analysis that treat scalars and vectors separately instead of combining them as in quaternions.

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

- Standard Basis Vectors i, j, k: 0:00
- Writing Vectors in Standard Basis Vector Form: 3:16
- Geometric Interpretation: 6:33
- Example 5: 12:34
- Historical Note on Quaternions: 16:43

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