Find the point of intersection of the lines.?

Question

Find the point of intersection of the lines:
X=1+2t, Y=-1, Z=t
and
X=3+2s, Y=s, Z=4+2s

Answer 1

You need X=X, Y=Y, Z=Z. From Y=Y we have s=-1, from Z=Z, t=2, and then from X=X, 5=1 which is not possible. Therefore the lines do not intersect. Check your equations.

Answer 2

Find the point of intersection of the lines:

L1: x = 1 + 2t, y = -1, z = t
and
L2: x = 3 + 2s, y = s, z = 4 + 2s

We have:

x = 1 + 2t = 3 + 2s
y = -1 = s
z = t = 4 + 2s

From y we have
s = -1

Plug into z.
t = 4 + 2s = 4 + 2*(-1) = 4 - 2 = 2
t = 2

Check with x.
1 + 2t = 3 + 2s
1 + 2*2 = 3 + 2*(-1)
1 + 4 = 3 - 2
5 = 1

This is false so the lines do not intersect.