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Zenmo

  • one year ago

(A) Find a set of parametric equations and (B) symmetric equations that passes through the given two points of a line. (-1/2, 2, 1/2), (1, -1/2, 0)

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  1. Michele_Laino
    • one year ago
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    how are defined symmetric equations?

  2. dan815
    • one year ago
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    probably just meants change them into z=f(x,y)

  3. Michele_Laino
    • one year ago
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    so we have to eliminate the parameter t, right?

  4. Michele_Laino
    • one year ago
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    please keep in mind that a line, in the euclidean space, is given as an intersection between two planes

  5. Michele_Laino
    • one year ago
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    so, all what we can do, is to solve the third equation for t, and then substitute that value of t into the first and second equation

  6. Michele_Laino
    • one year ago
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    namely: \[\Large t = \frac{1}{2} - z\]

  7. Michele_Laino
    • one year ago
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    I got: \[\begin{gathered} x = 1 - 3z \hfill \\ 2y = - 1 + 10z \hfill \\ \end{gathered} \]

  8. dan815
    • one year ago
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    |dw:1435138998149:dw|

  9. Michele_Laino
    • one year ago
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    So, your line is given by these equations: \[\Large \left\{ \begin{gathered} x + 3z = 1 \hfill \\ 2y - 10z = - 1 \hfill \\ \end{gathered} \right.\] As you can see those equations are the equations of two planes

  10. dan815
    • one year ago
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    u get which this is a line right, in euclian space

  11. dan815
    • one year ago
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    u were initially given the equation of a line in 3D <f(t),g(t),h(t)>

  12. dan815
    • one year ago
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    <x(t),y(t),z(t)> in that form

  13. Zenmo
    • one year ago
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    x=(-1/2)+3t, y=2-5t, z=(1/2)-t. Those are the solutions to part (A).

  14. Zenmo
    • one year ago
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    I want to eliminate the parameter, so X = Y = Z.

  15. dan815
    • one year ago
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    mhm right

  16. Zenmo
    • one year ago
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    |dw:1435132468871:dw|

  17. Zenmo
    • one year ago
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    The solution to symmetric is: \[\frac{ 2x+1 }{ 6 }=\frac{ y-2 }{ -5 }=\frac{ 2z-1 }{ -2 }\]. I don't know how to fix the x and z variable

  18. dan815
    • one year ago
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    well what looks like this is, it was isolated for t and set to each other

  19. dan815
    • one year ago
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    ah u removed the parametric form soo starting over then

  20. Zenmo
    • one year ago
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    Ok, I actually found it out. I just had to multiply 2 to the numerator and denominator of x and z to get rid of the fraction at the numerator

  21. dan815
    • one year ago
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    oh lol

  22. dan815
    • one year ago
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    i didnt know u were being picking about the simplification

  23. dan815
    • one year ago
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    i thought u just wanted to know how to get that form

  24. Zenmo
    • one year ago
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    yea i wanted to know how to convert x=(-1/2)+3t, y=2-5t, z=(1/2)-t into symmetric equations of X = Y = Z.

  25. dan815
    • one year ago
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    u did it already

  26. dan815
    • one year ago
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    you just isolate for t

  27. dan815
    • one year ago
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    and set them to each other

  28. Zenmo
    • one year ago
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    Yea, I just figured it out. Fractions are evil.

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