Finding the intersection points of the two lines in space

[macaulay]

given the lines in space

L1 : x = 2t + 1, y = 3t + 2, z = 4t + 3
L2 : x = s + 2, y = 2s + 4, z = -4s – 1
Find the point of intersection of L1 and L2.
How do i solve this?

 

[member 392791]

set the x's equal to each other and solve for either t or s, then plug into the other variables to get the coordinates

 

[paulfr]

Another method ....
Set the x's and y's equal to each other
2t+1 = s+2
3t+2 = 2s+4
solve the system for t and s
Plug the resulting values for t and s into
z=4t+3 and z = -4s-1
to be sure they give the same value for z
If they do not, the lines are skew
If they do, then the values for t and s give the
coordinates of the intersection point for x,y and z

 

[macaulay]

thank u very much mr. paulfr and woopydalan...i appreciate your replies to my question.. thank u very much =)