(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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- Zenmo

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- Michele_Laino

how are defined symmetric equations?

- dan815

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

- Michele_Laino

so we have to eliminate the parameter t, right?

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## More answers

- Michele_Laino

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

- 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

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

- Michele_Laino

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

- dan815

|dw:1435138998149:dw|

- 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

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

- dan815

u were initially given the equation of a line in 3D

- dan815

- Zenmo

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

- Zenmo

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

- dan815

mhm right

- Zenmo

|dw:1435132468871:dw|

- 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

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

- dan815

ah u removed the parametric form soo starting over then

- 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

oh lol

- dan815

i didnt know u were being picking about the simplification

- dan815

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

- 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

u did it already

- dan815

you just isolate for t

- dan815

and set them to each other

- Zenmo

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

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