# What is this vector problem asking?

1. Feb 4, 2014

### reddawg

1. The problem statement, all variables and given/known data
If r = <x, y, z> and r0 = <x0, y0, z0>, describe the set of all points (x, y, z) such that the magnitude of r – r0 = 4.

2. Relevant equations

3. The attempt at a solution

2. Feb 4, 2014

### PeroK

If you start by trying r0 = <0, 0, 0> does that help? Can you see what that means for r?

3. Feb 4, 2014

### reddawg

Trying that I get x2 + y2 + z2 = 16 after finding the magnitude, but I still can't see what that does to r.

4. Feb 4, 2014

### D H

Staff Emeritus
What kind of object does that equation describe?

5. Feb 4, 2014

### PeroK

What if you lose the z and reduce it to two dimensions: $$x^2 + y^2 = 16$$?

6. Feb 4, 2014

### reddawg

Including the z^2, the equation represents a sphere with radius 4. Without the z^2 it's a circle.

7. Feb 4, 2014

### PeroK

Good. And, if r_0 is the point <x0, y0, z0>?

8. Feb 4, 2014

### reddawg

I'm guessing that the reverse would be true making the components of r_0 negative, however squaring those would make that irrelevant. This is where I'm not following.

9. Feb 4, 2014

### PeroK

Think geometrically.

10. Feb 4, 2014

### reddawg

So r_0 is the center/origin of the sphere/circle?

11. Feb 4, 2014

### PeroK

Yes, that's it. $$|r - r_0| = 4$$ is the vector equation for a sphere of radius 4, centred at r0.

It's equivalent to $$(x-x_0)^2 + (y-y_0)^2 + (z-z_0)^2 = 16$$

12. Feb 4, 2014

### reddawg

Wow I way over thought this.

Thanks PeroK.