A Few Vector Questions

1. Jan 15, 2007

Physicus2

1. The problem statement, all variables and given/known data
I'm working with some 3-D vectors, which I'm a bit unsure about. I may have more of a clue than I think, but I could use a bit of assistance. So...

I'm dealing with two particles, A and B. A is on the x-y plane where x=y (*corrected: this was mistyped as x=7 when originally posted; it should be x=y) and is 20 meters from the origin, while B is on the y-z plane where y=z and is 40 meters from the origin. Write the two position vectors A and B in terms of their components, and the same for the displacement vector R that goes from A to B. Then, write a force vector F with magnitude 20 Newtons and pointing from A to B (also in component form).

3. The attempt at a solution

My initial and probably primary issue with this problem is determining where these two points are. I presume in digging through my thoughts that A is at point (20, 20, 0) and B (0, 40, 40). That would mean that my components are (for A) 20i + 20j and (for B) 40j + 40k. I'm not positive about this, though, and I'd appreciate some advice. As for the force vector, I realize I need to use (create) a unit vector to do this, but how do I create a vector that is in this 3-D form? My thought is that I could do this when I have the other vector components, but how do I use the magnitude (20 Newtons) in order to solve this?

Thank you for any assistance!

Last edited: Jan 15, 2007
2. Jan 15, 2007

AngeloG

It's a matter of actually drawing it out to solve for things =).

Such as the first part; x = 7 and is 20 meters away. We can use Pythagoreans theorem to this. x = 7, R = 20. a^2 + b^2 = c^2; b^2 = c^2 - a^2; b (This is y) = sqrt(20^2 - 7^2).

Then you have an idea of where it should be in the y direction =).

For A: [x y z] --> [7 y z]

It's just setting it up geometrically (using triangles) to understand where they are and applying some stuff here and there =). There's nothing too tricky about it, it's just how you go about doing your work.

Last edited: Jan 15, 2007
3. Jan 15, 2007

Physicus2

Thank you, that does help. I do unfortunately have to say that I apparently glossed over it in my proofreading, but the question should state that "x=y" and not "x=7." What does this do for the development of my triangle? Does that mean that the two sides are 20 and 20, since the point is 20 from the origin?

4. Jan 15, 2007

cristo

Staff Emeritus
No. You have a point A in the x-y plane, such that its distance from the origin in 20 and its x coordinate is equal to its y coordinate. So, one can construct a right angled triangle with sides x, y and 20 (where 20 is the hypotenuse). Try using Pythagoras' Theorem on this triangle to obtain x and y (remembering that x=y).

Last edited: Jan 15, 2007