## Linear Algebra- Finding the intersection of two straight lines.

1. The problem statement, all variables and given/known data

Determine whether the following two lines intersect:

(x-2)/2 = (y+3)/1 = (z-4)/-3 ,and (x+3)/4 = (y+4)/1 = (-z+8)/4

Find an intersection point, then find the distance between the lines.

2. Relevant equations
Symmetric equations of a straight line (given)
Parametric equations of a straight line.
AxB/mag(AxB)

3. The attempt at a solution

First I parametrized the equations and got :
x=1+2t x=-3+4t
y=-3+t y=4+t
z=4-3t z=8-4t

Then I found PQ and n and I am not sure what to do next to find the intersection point.
Thank You
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 Quote by tcanman 1. The problem statement, all variables and given/known data Determine whether the following two lines intersect: x-2/2 = y+3/1 = z-4/-3 ,and x+3/4 = y+4/1 = -z+8/4
parens parens parens.

For example x - 2/2 = x - 1, but that's clearly not what you mean.

The very first step in any math problem is to make sure you remove any ambiguity from your notation. That will help you avoid trivial mistakes.

 Tags distance, intersection, linear algebra, lines, parametric

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