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anonymous

  • 4 years ago

find a vector equation and parametric equations through the point (1,0,6) and perpendicular to the plane x + 3y + z =5

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  1. amistre64
    • 4 years ago
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    is the point on a line? thru the plane?

  2. anonymous
    • 4 years ago
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    ummm what?

  3. amistre64
    • 4 years ago
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    if so, the normal of the plance is the perp to it; strip off your coeefs for the line vector: <1,3,1> would be the vector that is perpenducular to the plane

  4. amistre64
    • 4 years ago
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    since 1,0,6 is not on the plane im going to assume its on the line perp to it (the perp line is called a normal)

  5. anonymous
    • 4 years ago
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    okay I'm with you so far

  6. amistre64
    • 4 years ago
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    x = Px + 1t y = Py + 3t z = Pz + 1t given the point (1,0,6) this makes x = 1 + 1t y = 0 + 3t z = 6+ 1t

  7. anonymous
    • 4 years ago
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    okay but why are the points (1,3,1) perpendicular to the plane?

  8. amistre64
    • 4 years ago
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    its a result of how the equation of a plane is defined

  9. amistre64
    • 4 years ago
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    the perp to the plane is a vector that dot producted to every line in the plane

  10. amistre64
    • 4 years ago
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    so given a point (Px,Py,Pz) in space: we can construct any vector from it by taking any random point (x,y,z) and subtracting the 2 of them: (x-Px, y-Py, z-Pz) is every vector that comes out from our point into space

  11. amistre64
    • 4 years ago
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    to elimante all the vectors that are not in a plane; we need to establish a perp vector to it so that when we dot it to these vectors we get 0, so all vectors of the form: (x-Px,y-Py,z-Pz) dot (Nx,Ny,Nz) = 0 Nx(x-Px) +Ny(y-Py) +Nz(z-Pz) = 0 is the equation of the plane

  12. anonymous
    • 4 years ago
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    okay makes sense!

  13. amistre64
    • 4 years ago
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    good :)

  14. anonymous
    • 4 years ago
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    you're way better at explaining things than my book...

  15. amistre64
    • 4 years ago
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    thats becasue im crazy lol

  16. anonymous
    • 4 years ago
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    lol, does normal mean perpendicular?

  17. mathmate
    • 4 years ago
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    yes.

  18. mathmate
    • 4 years ago
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    Actually, yes in this context. The word normal is used for other things in maths elsewhere.

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