# Thread: Parametric and symmetric equations

1. ## Parametric and symmetric equations

Find symmetric equations for the line through (4, -11, -7)
that is parallel to the line x = 2+5t, y = −1+ 1
3 t, z = 9−2t.

and

Find parametric equations for the line through (2, -2, 15)
that is parallel to the xz-plane and the xy-plane.

I broke the given line down into its original form (r1 plus t x the direction vector). It's clearly the direction vector that the line must be parallel to. I have the r1 vector and the point given in the prompt, but I'm not sure what to do next.

As for the second one, I figured I would want to take it as the line parallel to the line of intersection of the two planes, which would be the x-axis. Is this the right way to look at it? If so, what then?

2. Originally Posted by grejo
Find symmetric equations for the line through (4, -11, -7) that is parallel to the line x = 2+5t, y = −1+ 13t, z = 9−2t.
We can see that $<5,13,-2>$ is the direction vector of the line by reading the coefficients of the $t's$.

So the symmetric equation we want is $\displaystyle\frac{x-4}{5}=\frac{y+11}{13}=\frac{z+7}{-2}$.

3. Thanks, Plato. That's what I expected with that question, but I kept thinking I needed to do something with the r1 vector. Thanks for the clarifcation.