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

A.) Find the parametric equation for the line [itex]\overline{L}[/itex] through (2,-1,4) and perpendicular to the lines:

[itex]\overline{r_{1}}[/itex](t) = <1,2,0> + t<1,-1,3>

[itex]\overline{r_{2}}[/itex](s) = <0,3,4> + s<4,1,-2>

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

2. Relevant equations

3. The attempt at a solution

Part A

[itex]\overline{r_{1}}[/itex]X[itex]\overline{r_{2}}[/itex] = -1[itex]\overline{i}[/itex] + 14[itex]\overline{j}[/itex] + 5[itex]\overline{k}[/itex]

[itex]\overline{L}[/itex](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!

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# Homework Help: Vector lines

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