Correct form of Unit Vectors

[pugfug90]

Homework Statement

Find a unit vector in the direction of the given vector.
v=5i-2j

Homework Equations

[[v]]=square root of (V1^2 +V2^2)
v/[[v]]

The Attempt at a Solution

I went 100% simplification.. answer I got was <(5squareroot of 29)/29, (-2squareroot of 29)/29>

But the back of the book says its.. (1/(square root of 29))<5, -2>...

Is there any reason that the book didn't simplify further?
---
On another problem, in one not given in "standard unit vectors" (i and j)..
u=<0, -6>..
I went straight to simplifying it to <0, -1>..and book also has that.. then why didn't the book write it as (1/6)<0,-6> like the 1st problem?

Thanks

 

[FrogPad]

$$\frac{1}{\sqrt{29}} = \frac{1}{\sqrt{29}}\frac{\sqrt{29}}{\sqrt{29}}=\frac{\sqrt{29}}{29}$$

You have the same answer. For the second problem, that is just how the book is writing it. The author probably has a good reason for doing what they are doing, maybe he/she feels that it looks more readable as <0,-1> then having the factor in front. I mean the factor is not necessary right (For the <0,1> case)? What book are you using that represents vectors such with "<"?

 

[pugfug90]

?
<(5squareroot of 29)/29, (-2squareroot of 29)/29>
and
(1/(square root of 29))<5, -2>
Both have "<" and ">".. I'm asking why they didn't divide the vector into the square root like the 2nd problem..

Book is Precalculus with Limits: A Graphing Approach Third Edition, Houghton Mufflin
http://college.hmco.com/mathematics/larson/precalculus_limits_aga/3e/students/index.html [Broken]

 

[FrogPad]

?
<(5squareroot of 29)/29, (-2squareroot of 29)/29>
and
(1/(square root of 29))<5, -2>
Both have "<" and ">".. I'm asking why they didn't divide the vector into the square root like the 2nd problem..

Book is Precalculus with Limits: A Graphing Approach Third Edition, Houghton Mufflin
http://college.hmco.com/mathematics/larson/precalculus_limits_aga/3e/students/index.html [Broken]

They factored it out. It's a nice way of presenting a lot of things. Think of it this way.

(1) How long would it take you to draw a vector <1,0,-1>?

(2) How long would it take you to draw a vector <1/sqrt(29), 0/sqrt(29), -1/sqrt(29) ?

(3) How long would it take you to draw a vector 1/sqrt(29) <1,0,-1>?

(1) It wouldn't take very long right?
(2) That one is not difficult, it just will take a a little bit longer than (1) to draw.
(3) This again is not difficult, however, it will take you longer than (1) but not longer than (2).

Since (2) and (3) are equivalent and you will have to draw (2) or (3), then (3) is the better choice for representing the expression because it will take less time to draw. It's preference though. So write it how you want.

 

[pugfug90]

(2) How long would it take you to draw a vector <1/sqrt(29), 0/sqrt(29), -1/sqrt(29) ?

Umm.. Why do you have 3 things in that vector thing?

PS, I'm just asking to make sure so that it won't be marked wrong on upcoming tests.

 

[HallsofIvy]

Your problem is in two dimensions. Frogpad was giving vectors in 3 dimensions. (But using the same numbers so the vectors are NOT unit vectors!)

The real answer to your question, "Why didn't the book simplify further" is because they don't have to. They're the ones who made up the problem and no one is grading them. They perhaps also wanted to make it clear that the answer was just the original vector divided by its length.

As to the more important question, "Should you simplify?", the answer is go by what your teacher says. He is the one who will be giving you a grade!