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anonymous

  • 5 years ago

Why is the minimum distance from the plane x+2y+3z=6 to the origin, \[6\div\sqrt{1^{2}+2^{2}+3^{2}}\] and not just \[\sqrt{1^{2}+2^{2}+3^{2}}\]

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  1. amistre64
    • 5 years ago
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    the equation of the plane involves the 6 as well

  2. amistre64
    • 5 years ago
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    x+2y +3z -6 = 0

  3. amistre64
    • 5 years ago
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    the minimum distanceto the origin would be the point on the plane the is perped to the origin right?

  4. amistre64
    • 5 years ago
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    the normal vector appears to be <1,2,3> by looking at it

  5. anonymous
    • 5 years ago
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    yeah as far as i understand. But i don't get why you can't just take the modulus of the normal vector? where does the 6 come in?

  6. anonymous
    • 5 years ago
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    i got the same normal vector btw

  7. amistre64
    • 5 years ago
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    the modulus of the normal vector isnt necessarily the same vector that is pointing to the point from the origin

  8. anonymous
    • 5 years ago
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    but direction doesnt matter when i square negative values

  9. amistre64
    • 5 years ago
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    its not the direction you need to determine really; its the nearest point to the origin shich isnt the same

  10. amistre64
    • 5 years ago
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    if you take the normal vector and scale it fromthe origin to meet the plane; that should do ti

  11. anonymous
    • 5 years ago
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    should i just construct a line that goes through the origin and plane with the normal vector (1,2,3)

  12. anonymous
    • 5 years ago
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    then find the distance when i find the point

  13. amistre64
    • 5 years ago
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    i would yes

  14. anonymous
    • 5 years ago
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    this just seems to be a method thats a bit long, is there nothing simpler

  15. amistre64
    • 5 years ago
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    there prolly is a simpler method; but none that come to mind :)

  16. anonymous
    • 5 years ago
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    thanks nyways

  17. amistre64
    • 5 years ago
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    yw

  18. anonymous
    • 5 years ago
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    the distance from a point P1(x1,y1,z1) to th plane: ax+by+cz+d=0 is: D= /ax1+by1+cz1+d/ : sq.rt(a^2 + b^2+c^2) I can show you solution in full if you need it

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