Question

determine if the lines in each pair intersect. if so, find the coordinates of the point of intersection.

[x,y,z]=[6,5,-14]+s[-1,1,3]
[x,y,z]=[11,0,-17]+t[4,-1,-6]

Answer 1

Rewrite it as a linear system of equations and solve.

Answer 2

I wrote the parametric equations for both lines and set them equal to each other. I got t=0 and s=-5. But my book says that there is no answer since the lines can't intersect. The lines are not parallel.

Answer 3

They need not be parallel. This is 3-space not 2-space

Answer 4

they are not parallel tho. but how cant I know if they intersect or not?

Answer 5

As I said, rewrite it as a system of equations. If there is no solution then they do not intersect.

Answer 6

i did write them, and I did solve them and when I isolated for t and s, i got 0 and -5. but my book says they don't intersect

Answer 7

ummm whats that???

Answer 8

This isn't a linear algebra class?

Answer 9

no

Answer 10

this is a high school class and the only thing I have learned so far about this is parametric equation, vector equation, and standard equation

Answer 11

Well you must have made a mistake when you attempted to solve the system by substitution/elimination or whatever you did. Since there is no solution.

Answer 12

the way my book does it is that they give parallel lines and they find the parametric equation, then they sub the point from the first equation into the second and see if its distinct or coincident. Then they use substitution and find that they don't intersect.

Answer 13

Yes, but I'm trying to tell you this is the same as trying to solve a system of linear equations. I'm sure you've done this before in school.

Answer 14

in 3D, two lines need not be parallel to not intersect


notice that with t=0 and s=-5
you get the points [11,0,-17]+t[4,-1,-6]= [11,0,-17]
and [6,5,-14]+s[-1,1,3]= [6,5,-14]+[5,-5,-15]= [ 11,0,-29]

though the points share the same x and y coordinates, their z coordinates do not match. the lines never meet.