Going over parametric equations...help?

Question

johnweldon1993 · Answer

The path x = 2y = 3z = 6t is a _______ traveled with speed ____

How is this a line? I am just drawing a blank?

ganeshie8 · Answer

thats a line passing through origin
divide by 6 to change it into symmetric form

ganeshie8 · Answer

$$\large  \dfrac{x}{6} = \dfrac{y}{3} = \dfrac{z}{2}  $$

ganeshie8 · Answer

$$\large  \dfrac{x-0}{6} = \dfrac{y-0}{3} = \dfrac{z-0}{2}  $$

ganeshie8 · Answer

it passes through (0,0,0) and the direction vector is (6,3,2)

ganeshie8 · Answer

you may write it in parametric form as  (0,0,0) + t(6,3,2)

johnweldon1993 · Answer

Ahhh!!!! yeah completely drew a blank....not used to seeing x = y = z I'm used to seeing t = x + y - z.....etc...

yeah that's the form! thank you much @ganeshie8 !

ganeshie8 · Answer

np :)