1. Unit vector

Hey,

I just want to make sure I correctly understand unit vectors. I know they indicate units of length or magnitude, but how does that play out practically speaking? Take the following example.

x f(x)=x^2

1 1
2 4
3 9
4 16

And so on. In layman's terms, what is exactly going on there? It looks like a simple exponential expression, but is that correct? Probably not, because wouldn't you just write f(x)=x2 (squared)? I just don't quite get the whole concept...

What if it's f(x)=x^3? How does that play out?

2. Originally Posted by SeanC
Hey,

I just want to make sure I correctly understand unit vectors. I know they indicate units of length or magnitude, but how does that play out practically speaking? Take the following example.

x f(x)=x^2

1 1
2 4
3 9
4 16

And so on. In layman's terms, what is exactly going on there? It looks like a simple exponential expression, but is that correct? Probably not, because wouldn't you just write f(x)=x2 (squared)? I just don't quite get the whole concept...

What if it's f(x)=x^3? How does that play out?

Ummm... It's a function. For a given x value, you take the cube of it and that's the value of f(x).

What does this have to do with unit vectors??

-Dan

3. Originally Posted by topsquark
Ummm... It's a function. For a given x value, you take the cube of it and that's the value of f(x).

What does this have to do with unit vectors??

-Dan
Haha, now I feel like a genius. A buddy of mine said the "^" symbol is used to indicate a unit vector. Guess not, heh.

4. Originally Posted by SeanC
Haha, now I feel like a genius. A buddy of mine said the "^" symbol is used to indicate a unit vector. Guess not, heh.
hehe, no. "^" indicates powers.

who is this buddy of yours?

5. Originally Posted by Jhevon
hehe, no. "^" indicates powers.

who is this buddy of yours?
A math tutor, actually, hahahah. As it was over the phone, maybe he didn't understand what I was describing. I said shift+6...what is that?

Anyways, thanks for the clarification.

6. Originally Posted by SeanC
A math tutor, actually, hahahah. As it was over the phone, maybe he didn't understand what I was describing. I said shift+6...what is that?

Anyways, thanks for the clarification.
he may have been refering to a vertical or horizontal shift, did he say shift to the right/left, or just a vertical shift of +6. in that case, he means you take a graph and you shift it up by +6. this happens when you add 6 to a graph.

see the diagram below for an example. the red graph is x^2 and the blue is x^2 + 6, that is, x^2 shifted up by 6 units.

7. Originally Posted by Jhevon
he may have been refering to a vertical or horizontal shift, did he say shift to the right/left, or just a vertical shift of +6. in that case, he means you take a graph and you shift it up by +6. this happens when you add 6 to a graph.

see the diagram below for an example. the red graph is x^2 and the blue is x^2 + 6, that is, x^2 shifted up by 6 units.
Ah, I actually meant the symbol produced by pressing shift+6 (^), which I specified on the call. What you showed, however, does make sense.

8. Originally Posted by SeanC
Ah, I actually meant the symbol produced by pressing shift+6 (^), which I specified on the call. What you showed, however, does make sense.
haha, oh! ok now i feel like a genius

9. Originally Posted by Jhevon
haha, oh! ok now i feel like a genius
My mathematical ignorance wins again. :P

10. Originally Posted by SeanC
Haha, now I feel like a genius. A buddy of mine said the "^" symbol is used to indicate a unit vector. Guess not, heh.
For the record, it does, but not as you applied it. However I can think of no way for you to type it without using some kind of text editor.

For example:
$\hat{i}, \hat{j}, \hat{k}$
are the unit vectors in the x, y, and z directions, respectively.

-Dan

11. Originally Posted by topsquark
For the record, it does, but not as you applied it. However I can think of no way for you to type it without using some kind of text editor.

For example:
$\hat{i}, \hat{j}, \hat{k}$
are the unit vectors in the x, y, and z directions, respectively.

-Dan
Ah yes, I've seen that. Thanks for the clarification.