Finding parametric equation perpendicular to two lines and intersection with a plane

[Allenman]

Am I doing this right?

Homework Statement

A.) Find the parametric equation for the line $\overline{L}$ through (2,-1,4) and perpendicular to the lines:
$\overline{r_{1}}$(t) = <1,2,0> + t<1,-1,3>
$\overline{r_{2}}$(s) = <0,3,4> + s<4,1,-2>

B.) Determine the point of intersection of the line and the plane 2x+2y-3z = 12

Homework Equations

The Attempt at a Solution

Part A
$\overline{r_{1}}$X$\overline{r_{2}}$ = -1$\overline{i}$ + 14$\overline{j}$ + 5$\overline{k}$
$\overline{L}$(t) = <2,-1,4> + t<-1,14,5>

so in parametric form:
x = 2-t
y = -1+14t
z = 4+5t

I'm kinda confused because one is with respect to "t" while the other is with respect to "s." Does it matter? I haven't done Part B yet because I want to make sure the first part is good first.

Any help is greatly appreciated!

 

[flyingpig]

No it doesn't matter what the parameter is. It's probably better that they are different

 

[SammyS]

Yes, your result looks good.

I would write the parametric form of the line as an ordered triple. Maybe just a matter of taste.

 

[Allenman]

Thanks guys! =)