Finding distance using vector components

[LadyTwi]

Homework Statement

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?

Homework Equations

Unsure.

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.

 

[maladroit]

here's some reading for you to do that should help!
http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html

 

[LadyTwi]

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?

 

[maladroit]

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.

 

[LadyTwi]

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

 

[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,
$$distance = \sqrt{\vec{r}\dot\vec{r}}$$.

 

[LadyTwi]

Thank you! I have the answer now. =D