Zenmo
  • Zenmo
(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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Michele_Laino
  • Michele_Laino
how are defined symmetric equations?
dan815
  • dan815
probably just meants change them into z=f(x,y)
Michele_Laino
  • Michele_Laino
so we have to eliminate the parameter t, right?

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Michele_Laino
  • Michele_Laino
please keep in mind that a line, in the euclidean space, is given as an intersection between two planes
Michele_Laino
  • Michele_Laino
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
Michele_Laino
  • Michele_Laino
namely: \[\Large t = \frac{1}{2} - z\]
Michele_Laino
  • Michele_Laino
I got: \[\begin{gathered} x = 1 - 3z \hfill \\ 2y = - 1 + 10z \hfill \\ \end{gathered} \]
dan815
  • dan815
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Michele_Laino
  • Michele_Laino
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
dan815
  • dan815
u get which this is a line right, in euclian space
dan815
  • dan815
u were initially given the equation of a line in 3D
dan815
  • dan815
in that form
Zenmo
  • Zenmo
x=(-1/2)+3t, y=2-5t, z=(1/2)-t. Those are the solutions to part (A).
Zenmo
  • Zenmo
I want to eliminate the parameter, so X = Y = Z.
dan815
  • dan815
mhm right
Zenmo
  • Zenmo
|dw:1435132468871:dw|
Zenmo
  • Zenmo
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
dan815
  • dan815
well what looks like this is, it was isolated for t and set to each other
dan815
  • dan815
ah u removed the parametric form soo starting over then
Zenmo
  • Zenmo
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
dan815
  • dan815
oh lol
dan815
  • dan815
i didnt know u were being picking about the simplification
dan815
  • dan815
i thought u just wanted to know how to get that form
Zenmo
  • Zenmo
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.
dan815
  • dan815
u did it already
dan815
  • dan815
you just isolate for t
dan815
  • dan815
and set them to each other
Zenmo
  • Zenmo
Yea, I just figured it out. Fractions are evil.

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