Understanding Parametric and Symmetric Equations in 3-Space

[mikee]

Homework Statement

hello i just had a quick question, Supose there's a line in three space that is parralel to the xy plane but not any of the axes, what does this indicate about the parametric and symmetric equations in three space.

Homework Equations

The Attempt at a Solution

I am not positive on the answer but i was thinking for the parametric equation the direction vector would be perpendicular to the xz and zy plane and the normal vector for the xy plane would be parralel to any of the other planes

 

[rootX]

It confusing because you are using planes to describe the line.

One thing for sure, the direction vector would be (a,b,0)

I think they just want to see that you have 0 for z in the direction vector and
(x-x0)/a = (y-y0)/b = ?

 

[Defennder]

Yeah, I think it's best you post the question from the book, otherwise we won't know what exactly you're asking for.

 

[mikee]

Recall that there are three coordinates planes in 3-space. A line in R3 is parallel to xy-plane, but not to any of the axes. Explain what this tells you about parametric and symmetric equations in R3. Support your answer using examples. ok that's the full question