# How do I find a plane that contains two given lines?

Mauve

## Homework Statement

a. Find a point at where these lines intersect
b. Find the equation of a plane that contains the two lines.

## Homework Equations

r[/B] = <1,3,0> + t<3,-3,2>
r = <4,0,2> + s<-3,3,0>

## The Attempt at a Solution

I correctly found the point of intersection to be (4,0,2) for part a, but for some reason, I can't find the equation of the plane. I solved the cross product for <3,-3,2> and <-3,3,0> to get <-6,-6,18> and used that to find -6(x – 4) - 6y + 18(z – 2) = 0 as my equation, but that was marked incorrect. Is this an arithmetic issue or did I approach the problem the wrong way? I've gone over it numerous times and can't find the error.

## Answers and Replies

Staff Emeritus
Homework Helper
Gold Member
2021 Award
Double check your cross product.

Mauve
Double check your cross product.
So apparently 9 - 9 = 0 and not 18 and also I am a raging imbecile. Thank you very much for your input. It really did help

Staff Emeritus
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