Position, Displacement & Force Vectors: Solving 3D Vector Problems

[Physicus2]

Homework Statement

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).

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!

 

[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.

 

[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?

 

[cristo]

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).