# Find all algebraic vectors

1. Apr 4, 2016

### Physicaa

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

I don't think there is any equation related to this..
3. 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...

Last edited: Apr 4, 2016
2. Apr 4, 2016

### Staff: Mentor

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.

3. Apr 4, 2016

### 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.

4. Apr 4, 2016

### HallsofIvy

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

5. Apr 4, 2016

### Physicaa

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

6. Apr 5, 2016

### HallsofIvy

Staff Emeritus
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?

7. Apr 5, 2016

### Physicaa

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.

8. Apr 5, 2016

### Physicaa

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.