Thread: Finding the equation of a plane that contains two lines

I need help finding the equation a plane that contains the lines <t,2t,3t> and <3t,t,8t>
I don't really know where to start. I tried setting the two lines equal to each other to find a point of intersection but it turned out funky. Any help would be appreciated.

I found the solution in case anyone else has the same problem.

Lines intersect at origin O(0,0,0)
r: [t,2t,3t] = t[1,2,3] = t u
s: [3t,t,8t]=t[3,1,8] = t v

where
u = [1,2,3]
v = [3,1,8]

are the direction vectors of the lines

a vector which is normal to the plane containing r and s is
the cross product uxv

u x v = det([i, j, k; 1, 2, 3; 3, 1, 8])

u x v = 13i + j - 5k = [13,1,-5]

so the plane containing r and s has equation

13x + y - 5z = 0

Originally Posted by jtl4231

I need help finding the equation a plane that contains the lines <t,2t,3t> and <3t,t,8t>
I don't really know where to start. I tried setting the two lines equal to each other to find a point of intersection but it turned out funky. Any help would be appreciated.

It is clear that if then is on both lines.

Now the vector is the normal to the plane.