Question

(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)

Answer 1

how are defined symmetric equations?

Answer 2

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

Answer 3

so we have to eliminate the parameter t, right?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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