Solving the Homework: Parametric Equation and Point of Intersection

[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! =)