This question just seems somewhat unclear.
Asking for symmetric and parametric equations for the z axis means to have x and y equaling zero?
Hello, TJ2988!
You are expected to know this. . .Write the symmetric and parametric equations for the z axis.
A line through $\displaystyle P(x_1,y_1,z_1)$ with direction vector $\displaystyle \vec v \:=\:\langle a,b,c\rangle$ has:
. . Symmetric equation: .$\displaystyle \frac{x-x_1}{a} \:=\:\frac{y-y_1}{b} \:=\:\frac{z-z_1}{c}$
. . Parametric equations: .$\displaystyle \begin{Bmatrix}x &=& x_1+at \\ y &=& y_1 + bt \\ z &=& z_1 + ct\end{Bmatrix}$
We have: .$\displaystyle P(0,0,0)$ and $\displaystyle \vec v \:=\:\langle0,0,1\rangle$
. . Go for it!
Okay, so then the equations would be as follows:
Symmetric:
(x-0)/0 = (y-0)/0 = (z-0)/1
Parametric:
x=0
y=0
z=t
Although the symmetric equations of x & y are ÷ 0 which is not allowed. So how would do you change it so they are not?
Multiply all by zero to give x=y=0?
Thank you very much for your help!