Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

yw