Explain what this tells you about parametric and symmetric equations in R^3?

1. Jul 18, 2009

axxon

parametric and symmetric equations in R^3??

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

This question had me thinking for a while, but i want to confirm my understanding or if i am even correct.

I think the line is perpendicular to the Z-axis, So does this mean that the directional vector for z component is 0? basically [ax,ay,0].But couldn't it be perpendicular to xy plane, and still have a directional z component?
But besides that, using that information, in terms of parametric equation it tells us that
the z is just going to equal the position vectors z component.

Now here is where i get confused...with the symmetric equation.
Can you guys please explains this to me in simplest terms...i am trying really hard to understand this vectors in 3 space stuff.

Last edited: Jul 18, 2009
2. Jul 18, 2009

Pengwuino

Re: Explain what this tells you about parametric and symmetric equations in R^3??

To answer your first questions, yes, it's perpendicular to the Z-axis and there can be no value for the Z component other then 0, otherwise it wouldn't be perpendicular to your xy-plane. If it were perpendicular to the xy-plane, then by definition it would have a Z-component. However, the question is talking about being parallel to the xy-plane.

3. Jul 18, 2009

axxon

Re: Explain what this tells you about parametric and symmetric equations in R^3??

Ah alrite i just got that i decided to draw out a graph...yes what you said sums that up...now onto the parametric and symmetric equations

4. Jul 18, 2009

axxon

Re: Explain what this tells you about parametric and symmetric equations in R^3??

5. Jul 20, 2009

axxon

Re: Explain what this tells you about parametric and symmetric equations in R^3??

well can you answer the second part? am i atleast close?

6. Jul 20, 2009

HallsofIvy

Re: Explain what this tells you about parametric and symmetric equations in R^3??

Given x, y, z as parametric equations with parameter t, you can find the "symmetric" equations by solving each equation for t and setting them all equal. In this case, z is a constant: there is no t so you can't solve for t. The symmetric equations are an equation in x and y with the additional equation "z= constant".

7. Jul 20, 2009

axxon

Re: Explain what this tells you about parametric and symmetric equations in R^3??

So Symmetric would look like:
$$\frac{x-ax}{bx}$$= $$\frac{y-ay}{by}$$= az
(where 'az' is a constant)