Visualizing the Span of Two Vectors in 3-Space

An Interactive Applet powered by Sage and MathJax.

(By Prof. Gregory V. Bard, based on a suggestion by Sepideh Stewart. Updated by Ryan G. Hornberger.)


On this page, we're going to try to visualize the span of 2 vectors in ordinary 3-dimensional space.


Now we've going to see what the span looks like for 2 particular vectors, and it turns out that it is a plane in most cases. However, if the two vectors happen to be linearly dependent then it will be a line.

The neat thing about this applet is that you can drag the picture around and view it from many different angles. Also, you can change the vectors used.


Last modified on June 8th, 2022.