# Finding distance using vector components

1. Oct 11, 2009

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

With reference to Fig. 3 (not accurate), where the origin is at the centre of the image, if r1 = (0.10)î+(-0.80)j hat, and r2 = (-0.90)î+(0.10)j hat, what is the distance between the dots?

2. Relevant equations

Unsure.

3. The attempt at a solution

I'm not so good with these i hat and j hat vector components. I've tried using (x2-x1) + (y2-y1) but that didn't give the correct answer. I'm not really sure what I can do with the two equations.

2. Oct 11, 2009

3. Oct 11, 2009

That is a helpful link, however I still can't get the answer. XD Do I have to find the angle between r1 and r2 and use that to find the distance or does it have to do with the addition of the i hat components and the j hat components?

4. Oct 11, 2009

the beauty of unit vectors is that it already takes the angle into consideration! all you have to do in this case is add the i vectors with i vectors and js with js.

5. Oct 11, 2009

I've tried that but BLS/CAPA is still telling me that my answer is wrong. Maybe I'm entering it wrong...?

6. Oct 11, 2009

### UgOOgU

The distance between two points is the magnitude of the vector connecting these two points. In your problem this vector is $$\vec{r} = \vec{r_{2}}-\vec{r_{1}}$$. To encounter the magnitude of this vector, all we have to do is calcute the scalar product of it with itself and take the square root. So,
$$distance = \sqrt{\vec{r}\dot\vec{r}}$$.

7. Oct 12, 2009