# Talk:Vector

## Checklist

This page didn't have the text in the beginning. I edited a little out in the sections that were there originally.

My comments are in red. AnnaP 7/7

Messages to the Future

• No comments to anyone in the future. Maybe, someone might want to go more in detail with unit vectors.

References and footnotes

• Didn't really use any source. just own knowledge and the previous writer didn't provide references either.

Good writing

• tried to get rid of awkward phrases. Hopefully everyone is understandable and simple.

Quality of prose and page structuring

• I provided reason and tried to make smooth transitions to other subtopics in order to understand things clearly.
• Head titles show where the page is going.

Integration of Images and Text

• Few images are provided and referred to.
• Images are used to explain the streching and shrinking of vectors and there is a nice applet that was already provided.
• Used multiple math syntax to express vectors.

Mathematical Accuracy

• As with your dot product page, I'd encourage using regular parentheses or square brackets to denote vectors. Regular parentheses would be nice because some of the older text of the page uses those

Layout

• Text is in short paragraphs.
• looks fair in many windows.
• Hide over feature is used in constructing vector and their properties.
• Try to play around with the size and location of the images in the first section. They are a bit small and the text gets broken up by the images when I make my browser window anything but full-sized. I also suggest moving image 2 down much lower to where you actually talk about all three of the standard unit vectors.

I am formatting some of Steve Cunningham's pages, and he wrote a page called Vectors as well. I'm not sure if you've seen it or not, but I'm not exactly sure what to do with it. Would you like a copy so you can make any changes from his paper (if you want them made at all). I see that you are actively working on this page, so I don't want to mess with it.

Nordhr 17:36 7 July 2011

Kate 15:15, 13 June 2011 (UTC): I think it's looking pretty good!

• You asked about the pictures - I think the main problem is your text doesn't refer to them. The reason they feel randomly placed is because you don't make the connections between the picture and what you're talking about explicit. For example, right after you talk about the vector (3,3,2), you should tell the reader to look at the picture that graphs that vector.[CHECK Leah]
• Rebecca 16:46, 15 June 2011 (UTC) Great first paragraph! Very clear.
• xd 14:17, 22 June 2011 (UTC) Generally, very good. A minor thing is that this page is strictly Euclidean space vectors so you can just briefly mention that.
• Diana 6/30/11 10:40: This is a great page! Very clear. There are places, though, where the writing is a bit confusing or choppy in style. I realize this is both a tangential aspect of conveying the math and a very broad, unspecific comment, but perhaps you could try reading the page aloud to yourself to see where you could smooth out the language. Here's an example of the sort of thing I'm talking about:
"A unit vector is denoted by a lowercase letter with a hat above it, like so, $\hat{a}$. It is pronounced as a-hat."

This seems awkward; the second comma in the first sentence would work better as a colon, and "It is pronounced as a-hat" would make more sense if it were, "It is pronounced, 'a-hat.'"

These are just ideas -- obviously, the style should be your own, but I think you could make the writing "flow" a bit better.

## Vector

• Rebecca 16:45, 15 June 2011 (UTC) I think you need to be a bit more explicit when you introduce the idea of coordinate systems. It might be nice add another image here. I imagine you adding a duplicate of the picture you already have (of the blue vector), but in this image you label the point (like maybe (2,3)) and add the x,y axis. Then you can talk about how assigning x and y coordinates to a vector allows us to be more precise when we talk about vectors. "So if we have an arrow we can now communicate with someone else about how much the vector goes in the x direction, the y direction and the z direction by using unit vectors." And actually, I would stick to just x and y at first to keep it simple. Then maybe introduce more dimensions later? Just an idea. [CHECK]
• I found your second paragraph a little disjointed. You use component notation to explain unit vector notation, and then explain what component notation is. I'd change the order that you explain the two notations in, and also connect your (3,2) example to the picture you have of it. I moved the sentences that you had around, so that you can see what I'm trying to say:[CHECK Leah]
When we have a vector quantity we put an arrow on top of the labeling letter to remind us that it is a vector. It looks like so: $\vec A$. One way of writing vectors is by components, like this: $\vec A = \left \langle a_1, a_2, a_3 \right \rangle$. The components of a vector can also be are written as: $\begin{bmatrix} 3 \\ 2\\ \end{bmatrix}$. This vector has an x-component of 3 and a y-component of 2, and is shown in the image to the bottom right. With $\left \langle a_1, a_2, a_3 \right \rangle$ as any numerical values we can also write any vector in terms of standard unit vectors: $\vec A = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$.

• I think you should move the old information down on the page, so that when it's unhidden it starts all the way over on the left-hand side and doesn't have to move around your pictures.[CHECK Leah]
• Where did the adding and subtracting vectors applet go? I really liked it! Was there a reason you deleted it, or was it just an accident?[The applet wasn't working on my laptop so I thought it wasn't working at all. I must not have the right software. But I did add it in Leah ]

• Rebecca 20:33, 26 June 2011 (UTC)I would move the section below to before the sentence "In order to give a vector's position using unit vectors, we write it as a combination of unit vectors that are placed along the the coordinate axes." This way, you introduce the topic, give it's notation, and then you can talk about how it's used. Also the sentence "our standard correspond to the x-y-z coordinate system" is confusing.. try rewording that.
"A unit vector is denoted by a lowercase letter with a hat above it, like so, $\hat{a}$. It is pronounced as a-hat. Our standard correspond to the x-y-z coordinate system. $\hat{i}$ points along the x-axis $\hat{j}$ points along the y-axis and $\hat{k}$ points along the z-axis. This notation is used in physics, engineering and linear algebra.

• I think this paragraph is a little confusing...
Referring to Image 2 on the right, we express a vector in terms of its components relying on the unit vectors. This helps us understand the direction. As for the magnitude, the length of a vector, we can just measure its length. The magnitude is denoted by $\left| \vec A \right|$. The magnitude of a vector is a scalar quantity, a numerical value with no direction.
• I think this is a bit confusing. You might try to reword it? Maybe some of the other imagers could help. It might also be helpful to return to your example for [6,8] to help them understand using unit vectors. You could talk about how you would need 6 unit vectors going in the x direction and 8 unit vectors going in the y direction to make that vector.

Leah 14:58, 27 June 2011 (UTC) Did Rebecca's suggestions.

*Diana 6/30/11 11:03: In the last paragraph, you explain very well what unit vectors are and say that they can be used to express a vector, but you don't give an example of how to use them to express vectors until the next section. This is a bit confusing. Could you maybe just give a quick example using "image one" in this paragraph, and point readers to the next section for more details?

## Labeling Vectors

*Rebecca 20:45, 26 June 2011 (UTC) I think this section is very good. It's nice to be able to see all the different labeling options next to each other. However, i would suggest that you show each option for the same vector. All you would have to do to show this is

When we have a vector quantity we put an arrow on top of the labeling letter to remind us that it is a vector. It looks like so $\vec A$. One way of writing vectors is by components, like this: $\left \langle a_1, a_2 \right \rangle$. For example, suppose we want to write a specific vector in components, and we know the vector goes 3 units in the x direction and 2 units in the y direction. Then we can simply write: $\left \langle 3, 2 \right \rangle$. The components of the same vector can also be written as: $\begin{bmatrix} 3 \\ 2\\ \end{bmatrix}$. This vector has an x-component of 3 and a y-component of 2, and is shown in the image on the right.

With $\left \langle a_1, a_2, a_3 \right \rangle$ as any numerical values we can also write any vector in terms of standard unit vectors: $\vec A = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$. If we are given $\vec A = 3 \hat{i} + 3 \hat{j} + 2 \hat{k}$ we know that vector A is 3 units in the x and y direction and 2 units in the z direction. This vector could equivalently be written as $\left \langle 3, 3, 2 \right \rangle$ or $\begin{bmatrix} 3\\ 3\\ 2\\ \end{bmatrix}$. It is shown in the image below.
• I think all your hidden sections are very clear. My only suggestion is to try and more the pictures around so the bullets line up a little better and the page is easier to read. Otherwise, it looks great!

Leah 14:57, 27 June 2011 (UTC) Did Rebecca's suggestions.

*Diana 6/30/11 11:03: You're missing the "$...$" marks in your second paragraph for one of your vector notations. It's just showing up as code.

#### Anna 7/9

Now in a totally awake state, I realize that anyone who needs to click over to a helper page on vector isn't going to see a d as meaning a total differential. So strike that part of my comment below.

#### Anna 7/7

It's so much prettier now! I love it. The only thing you could, maybe, possibly change is not using a d as one of your scalars. I know you call it a scalar at the beginning, but for some reason when I was looking at it, I kept seeing a totally differential. (Though, that may be due to the fact that I'm tired).

#### Anna 7/6

I realized that you don't actually list properties in the algebraic explanation right after you say that "Vectors are any mathematical entity which have the following properties" You might want to reorganize that section a bit. I think all of your words are good... just the structure and order should change.

#### Anna 7/4

Could you explain your stretching and rotating picture more thoroughly?

#### Gene 6/27

Hey, Brendan,

I think you need to have a section on vectors as arrows, since that's something that folks will run into. Also some 3D vectors.