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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

how are defined symmetric equations?

2. dan815

probably just meants change them into z=f(x,y)

3. Michele_Laino

so we have to eliminate the parameter t, right?

4. Michele_Laino

please keep in mind that a line, in the euclidean space, is given as an intersection between two planes

5. 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

6. Michele_Laino

namely: $\Large t = \frac{1}{2} - z$

7. Michele_Laino

I got: $\begin{gathered} x = 1 - 3z \hfill \\ 2y = - 1 + 10z \hfill \\ \end{gathered}$

8. dan815

|dw:1435138998149:dw|

9. 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

10. dan815

u get which this is a line right, in euclian space

11. dan815

u were initially given the equation of a line in 3D <f(t),g(t),h(t)>

12. dan815

<x(t),y(t),z(t)> in that form

13. Zenmo

x=(-1/2)+3t, y=2-5t, z=(1/2)-t. Those are the solutions to part (A).

14. Zenmo

I want to eliminate the parameter, so X = Y = Z.

15. dan815

mhm right

16. Zenmo

|dw:1435132468871:dw|

17. 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

18. dan815

well what looks like this is, it was isolated for t and set to each other

19. dan815

ah u removed the parametric form soo starting over then

20. 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

21. dan815

oh lol

22. dan815

i didnt know u were being picking about the simplification

23. dan815

i thought u just wanted to know how to get that form

24. 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.

25. dan815

u did it already

26. dan815

you just isolate for t

27. dan815

and set them to each other

28. Zenmo

Yea, I just figured it out. Fractions are evil.

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