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Construct a geometric figure that illustrates why a line in $\mathbb{R}^{2}$ not through the origin is not closed under vector addition.

Therefore, addition of vectors upon the line $y=4 x+7$ does not obey closure law.

Calculus 3

Chapter 4

Vector Spaces

Section 1

Vector Spaces and Subspaces

Vectors

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

02:56

In mathematics, a vector (…

06:36

02:12

Parallel line and plane Sh…

07:10

Prove that $r$ describes a…

04:07

Determine whether the give…

01:10

Find a vector a with repre…

02:50

01:46

Show that every line that …

01:00

Let $R$ be a closed bounde…

01:47

08:21

02:36

Give a geometric descripti…

this video, we're gonna be a solving problem. Number four of section four point win. Um, and it asks us to construct a geometric figure that illustrates why align in our two would, um that is that does not pass through the origin would not be closed under avec tradition. So, um, are to just means that in just a regular graph, So, like with two coordinates X y. And if you just take a graph and draw any line that is not through the origin, let's say this is 10 and this is zero negative one, um, for for ah line or for a set of points to be closed under vector addition, they need to be there. Ah, there. When you add them together, they have to be the result. The result has to be on the line for it to be closed under vector edition. So if you call this a and if you call the second point B, a plus B will have to be on the lion, which means that one common zero plus zero common negative one. We'll have to be on the line, which is one come on, negative one, which will have to be on the line for it to be closed under, um, Vector Edition. One common negative one, however, is, um is not on the line as it is right here. The point I drew on the graph just now, and it is not part of the line that that passes through zero negative 110 Therefore, um, therefore are too. In this particular case, would is not closed. So it's open under vector addition, and this is the same Would, um, any line that is not centered at zero as

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