Point of intersection of two lines

[dcramps]

Homework Statement

Find the point of intersection of two lines
x = -9 + 5t
y = 1 + t
z = 10 - 4t

and

x = -2 -3t
y = 5 + 2t
z = 5 + 3t

Homework Equations

N/A

The Attempt at a Solution

I have read that you should set two of the equations equal to find the value of t, and that value of t should hold for the third equation, but whenever I do that I get two different values for t, and neither of them hold up in the third equation. What am I doing wrong?

 

[tiny-tim]

Hi dcramps!

Where the two lines intersect, the parameter t will be different on each line.

So call the parameter for the second line u, then set two of the equations equal to find the values of t and u.

 

[dcramps]

Thanks! Now I have my t and u values, and plugging them into the third equation gives me equality...but where do I go from here? Do I plug them into all of the original equations and use the results as my intersection point?

 

[tiny-tim]

Yup!

 

[dcramps]

Excellent. Thanks for your help :)