Question

Find the intersection, if any, of the line x=t, y=1+2t, z=3-t and the line x=-3, y=-6+2u, z=3-6u?

Answer 1

I know it is not parallel so it would have to be either skew, or intersect at a point...

Answer 2

What's the question? It's confusing. Due you want point of intersection where all those lines or what? Explain what you want and I can help.

Answer 3

To find out how I can determine whether the lines are skew or if they intersect at a point.

Answer 4

suppose they instersect
y= 1+2t = -6+2u
z = 3-6u = 3-t
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we get two linear equations
3-6u = 3-t
1+2t = -6+2u
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solving them we get
http://www.wolframalpha.com/input/?i=solve+1%2B2t+%3D+-6%2B2u%2C+3-6u+%3D+3-t
t = -21/5, u =-7/10
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we have for x=t and x=3
or x=-21/5 and x=3

so they are not equal points, hence they do not intersect.


Note* I'm not quite sure on this

Answer 5

Wolf say's no solution exist http://www.wolframalpha.com/input/?i=solve+x%3Dt%2C+y%3D1%2B2t%2C+z%3D3-t%2C++x%3D-3%2C+y%3D-6%2B2u%2C+z%3D3-6u

Answer 6

I think lines are suppose to be skew...

1. x: t=-3

2. y: 1+2t=-6+2u
2t-2u=-7

3. z: 3-t=3-6u
-t+6u=0

Answer 7

1. + 2.

t=-3
-t+6u=0
----------
6u=-3
u= -1/2

Answer 8

what's skew??

Answer 9

Skew lines are two lines that do not intersect but are not parallel...

Answer 10

Oh ... neither parallel now intersecting right??
you know how to find parametric equation right??

the above method provides that it has no solution


for skewness write the parametric equation