Identifying Algebraic Vectors in Two Dimensions

[Physicaa]

Homework Statement

[/B]
Find all algebraic vectors of $$R^2$$ r (r is a vector) such that

$$\frac{\mathbf{r}}{\lvert\lvert \mathbf{r}\rvert\rvert} = (\frac{1}{2}\sqrt{2}, \frac{1}{2}\sqrt{2})$$

Homework Equations

I don't think there is any equation related to this..

The Attempt at a Solution

The only thing I can determne from this is that this :
$$\frac{\mathbf{r}}{\lvert\lvert \mathbf{r}\rvert\rvert}$$

is unitary according to one theorem that I have in my book as long as the vector r isn't equal to 0. Other than that, I'm not really sure what to do...

 

[Mark44]

Homework Statement

[/B]
Find all algebraic vectors of $$R^2$$ r (r is a vector) such that

$$\frac{\mathbf{r}}{\lvert\lvert \mathbf{r}\rvert\rvert} = (\frac{1}{2}\sqrt{2}, \frac{1}{2}\sqrt{2})$$

Homework Equations

I don't think there is any equation related to this..

The Attempt at a Solution

The only thing I can determne from this is that this :
$$\frac{\mathbf{r}}{\lvert\lvert \mathbf{r}\rvert\rvert}$$

If you divide a vector by its magnitude, you get a unit vector with the same direction as the original vector.
The problem is asking for all vectors that have the same direction as the one you show in the problem statement section.

is unitary according to one theorem that I have in my book as long as the vector r isn't equal to 0. Other than that, I'm not really sure what to do...

 

[BvU]

Hi,
Yes, $\left |{\vec r\over ||\vec r|| } \right | = 1$ for any vector $\vec r = (a, b)$. Now write out the quotient for this last $(a,b)$ and that might lead you to a condition relating a and b !

PS there is a difference between unity and unitarity. You meant unity.

 

[HallsofIvy]

I an a bit puzzled as to what is meant by "algebraic" vectors. How do algebraic vectors differ from ordinary vectors?

 

[Physicaa]

I an a bit puzzled as to what is meant by "algebraic" vectors. How do algebraic vectors differ from ordinary vectors?

I don't know. That's a good question.

 

[HallsofIvy]

This was your problem! How can you hope to solve a problem, or even know if an answer is correct, if you don't know what the question is asking?

 

[Physicaa]

This was your problem! How can you hope to solve a problem, or even know if an answer is correct, if you don't know what the question is asking?

I don't think the question is asking me to tell the difference between an ordinary vector and an algebraic one. I was just saying that I frankly don't know how the two are different, I always saw them as the same. I think algebraic just refers to vectors with coordinates but I'm not sure tbh.

 

[Physicaa]

This was your problem! How can you hope to solve a problem, or even know if an answer is correct, if you don't know what the question is asking?

I don't think the question is asking me to tell the difference between an ordinary vector and an algebraic one. I was just saying that I frankly don't know how the two are different, I always saw them as the same. I think algebraic just refers to vectors with coordinates but I'm not sure tbh.