The geometric shape of parametric equations

[Kubilay Yazoglu]

Hello everyone, I have another question mark buzzing inside my head.

After the elimination steps of a matrix, I'm having some problems about imagining in 3D.

For example, x=t , y=2t, z=3t what it shows us?

Or, x=t+2, y=t,,z=t ?
Or another examples you can think of. ( Complicated ones of course)

Thank you.

 

[mfb]

Plug in t=0, t=1, t=2 and see what you get, that should help.
If possible, you can also solve one of the equations for t and plug it into the other two equations then you get y(x), z(x) or similar.

If all three equations are linear, the result is always a straight line.