Question

!!Urgent question!! Quick help is greatly appreciated

Determine if lines L1 and L2 are skew. If so, what is the distance between them? (Equations of L1 and L2 attached.)

Answer 1

L1: \[\frac{ x-1 }{ -1 }=\frac{ y-3 }{ -2 }=\frac{ z-1 }{ -3 }\]

L2:\[\frac{ x-1 }{ 1 }=\frac{ y+4 }{ 3 }=\frac{ z-2 }{ -7 }\]

Answer 2

@Compassionate Kind of stuck. I know the lines are skewed, but do not know how to find the distance between them?

Answer 3

Oh, sorry, but I haven't taken this class yet. Sorry! Let me tag other people who might be able to help.

@bahrom7893 @radar @thomaster

Answer 4

Ok, no problem.

Answer 5

Since the lines are skewed they can be viewed as lying on two parallel planes. The distance between the lines is the same as the distance between the planes.

Answer 6

Write line 1 as parametric equations: x=1+t, y=3-2t, z = 1-3t and line 2 is x=1+u, y=-4+3u, z=2-7u.

Answer 7

Ok, I've gotten that far, but how do I find the distance? Is it a distance equation using vectors?

Answer 8

The vectors describing the two lines directions are v1 = 1i - 2j-3k and v2= 1i+3j-7k.

Answer 9

The common normal vector to the two planes that contain the lines have to be orthogonal to those two vectors. So find v1 X v2

Answer 10

Cross product?

Answer 11

Yes!

Answer 12

And that is the distance?

Answer 13

No ... then you have to pick a value of t to get a point on the L1 (the first line) say t = 0 so a point on L1 would be (1,3,1) then you can get an equation for the P1 (the plane that L1 is in) by using the vector from the cross product and the point (1,3,1).

Answer 14

Then get a point on L2 by picking a value for u, say u = 0, so a point on L2 is (1,-4,2). Now the distance between this point and the Plane1 is the same as the distance from L1 and L2. You should have a formula for the distance between a point and a plane.

Answer 15

I don't understand what you mean...

Answer 16

Ok so what did you get for v1 x v2?

Answer 17

@Shhot ?

Answer 18

hold on. sorry.

Answer 19

23i+10j-5k

Answer 20

Oh man ... that is not what I got... you cross multiplied (i-2j-3k) x (i+3j-7k)? Double check your work and i'll double check mine.

Answer 21

yep, I got the same

Answer 22

Check your signs...on j and k.

Answer 23

Isn't that right?

Answer 24

Tell me if this is how you set it up?...