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What is this vector problem asking?

  1. Feb 4, 2014 #1
    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
    I don't know what this problem is asking to even attempt a possible solution. Please help?
     
  2. jcsd
  3. Feb 4, 2014 #2

    PeroK

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    If you start by trying r0 = <0, 0, 0> does that help? Can you see what that means for r?
     
  4. Feb 4, 2014 #3
    Trying that I get x2 + y2 + z2 = 16 after finding the magnitude, but I still can't see what that does to r.
     
  5. Feb 4, 2014 #4

    D H

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    What kind of object does that equation describe?
     
  6. Feb 4, 2014 #5

    PeroK

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    What if you lose the z and reduce it to two dimensions: $$x^2 + y^2 = 16$$?
     
  7. Feb 4, 2014 #6
    Including the z^2, the equation represents a sphere with radius 4. Without the z^2 it's a circle.
     
  8. Feb 4, 2014 #7

    PeroK

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    Good. And, if r_0 is the point <x0, y0, z0>?
     
  9. Feb 4, 2014 #8
    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.
     
  10. Feb 4, 2014 #9

    PeroK

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    Think geometrically.
     
  11. Feb 4, 2014 #10
    So r_0 is the center/origin of the sphere/circle?
     
  12. Feb 4, 2014 #11

    PeroK

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    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 $$(x-x_0)^2 + (y-y_0)^2 + (z-z_0)^2 = 16$$
     
  13. Feb 4, 2014 #12
    Wow I way over thought this.

    Thanks PeroK.
     
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