[SOLVED] Write parametric and symmetric equations for the z-axis.

**TJ2988** · March 12th 2009, 06:37 AM

This question just seems somewhat unclear.

Asking for symmetric and parametric equations for the z axis means to have x and y equaling zero?

**Soroban** · March 12th 2009, 07:27 AM

Hello, TJ2988!

Write the symmetric and parametric equations for the z axis.

You are expected to know this. . .

A line through $P(x_1,y_1,z_1)$ with direction vector $\vec v \:=\:\langle a,b,c\rangle$ has:

. . Symmetric equation: . $\frac{x-x_1}{a} \:=\:\frac{y-y_1}{b} \:=\:\frac{z-z_1}{c}$

. . Parametric equations: . $\begin{Bmatrix}x &=& x_1+at \\ y &=& y_1 + bt \\ z &=& z_1 + ct\end{Bmatrix}$

We have: . $P(0,0,0)$ and $\vec v \:=\:\langle0,0,1\rangle$

. . Go for it!

**TJ2988** · March 12th 2009, 07:35 AM

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!

**HallsofIvy** · March 12th 2009, 04:05 PM

Originally Posted by TJ2988

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?

Yes, that is exactly right.

Thank you very much for your help!

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