Symetric Form of a Line in R3

**sinewave85** · September 23rd 2010, 05:57 PM

This should be a simple one:

I know that the formula is

$\frac{x-x_{0}}{A} = \frac{y-y_{0}}{B}=\frac{z-z_{0}}{C}$

so long as A, B, and C are all non-zero numbers. But what if one of the direction numbers is zero? Do you just drop that part of the equation since it is undefined? For instance, if C is 0, then

$\frac{x-x_{0}}{A} = \frac{y-y_{0}}{B}?$

Or is the whole equation undefined?

**Soroban** · September 23rd 2010, 09:33 PM

Hello, sinewave85!

This should have been explained to you . . . at some time, by someone.

I know that the formula is : . $\displaystyle \frac{x-x_{0}}{a} \:=\: \frac{y-y_{0}}{b}\:=\:\frac{z-z_{0}}{c}$

But what if one of the direction numbers is zero?
Do you just drop that part of the equation since it is undefined? .No

Suppose the direction contains a zero: . $\vec v \:=\:\langle 2,3,0\rangle$

Believe it or not, we are allowed to write this:

. . . . . $\displaystyle \frac{x-x_o}{2} \;=\;\frac{y-y_o}{3}\;=\;\frac{z-z_o}{0}$

The standard "excuse" is that those denominators are simply "holders"
. . for the components of the direction vector.

So that we are not really dividing by zero,
. . we're just "storing" the zero there. . . LOL!

**sinewave85** · September 24th 2010, 04:58 AM

Divide by zero: shocking! Thanks so much.

(My text book only defines the equation for A, B, C explicitly all nonzero and nothing in my course material expanded on that.)

**xxp9** · September 24th 2010, 05:40 AM

the equation would be (x-x0)/A = (y-y0)/B, z=z0

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