Find an equation of the plane that contains the lines given by:
$$\frac{ x-1 }{ -2 }=y-4=z$$
and
$$\frac{ x-2 }{ -3 }=\frac{ y-1 }{ 4 }=\frac{ z-2 }{ -1 }$$

Question

Find an equation of the plane that contains the lines given by:
$$\frac{ x-1 }{ -2 }=y-4=z$$
and
$$\frac{ x-2 }{ -3 }=\frac{ y-1 }{ 4 }=\frac{ z-2 }{ -1 }$$

sirm3d · Answer

line 1: $$\frac{x-1}{-2}=\frac{y-4}{1} = \frac{z-0}{1}$$
the vector representation of the line is $$<-2,1,1>$$

the cross product the the two vector representations of the two lines is the vector normal to the plane containing the two lines

psymon · Answer

Alright, so the cross product gives me <-5,-5,-5>. Now just pick off a point from one of the symmetric equations?

sirm3d · Answer

yup, assuming that the lines are coplanar.
you should verify first if the lines are coplanar, that is, find the point of intersection.

psymon · Answer

Ah. Yeah, was wondering why they were finding that point. Alright, I think I can confirm that part on my own. Thanks ^_^

sirm3d · Answer

yw