Conclusions from Symmetric Equations Identity

[harrietstowe]

Homework Statement

What conclusion can be drawn from the lines (x-x₀)/a = (y-y₀)/b = (z-z₀)/c
(x-x₀)/A = (y-y₀)/B = (z-z₀)/C
if aA + bB +cC = 0

Homework Equations

The Attempt at a Solution

I put everything in parametric form but that didn't do much for me. Is it just that they are the same line because that has been my gut feeling.

 

[lanedance]

how about trying to think about normal vectors?