Dalia S.

Find the point of intersection of the two lines

Consider the two lines
L1:  x = -2t, y = 1 + 2t, z = 3t
and
L2:  x = -9 + 5 s, y = 5 s, z = 2 + 4 s

Find the point of intersection of the two lines.

By: Tutor
5.0 (44)

Math and Science Tutor with an Engineering Background

Dalia S.

by adding the two first equations i get 1=s, I'm a bit confused as to what to do next if you don't mind explaining
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10/27/14 Byron S.

When you've found your value for s, you can substitute it into your parametric equations for line 2. You also can solve for t in any of the equations, and plug that value into line 1.

Lets use your value of s=1:
L2: x = -9+5(1) = -4
y = 5(1) = 5
z = 2+4(1) = 6
(-4, 5, 6)

To check, we need to make sure that line 1 also passes through this point:
-2t = -9+5(1)
-2t = -4
t = 2

L1:
x = -2(2) = -4
y = 1+2(2) = 5
z = 3(2) = 6
(-4, 5, 6)

This is the solution!
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10/27/14

Dalia S.

perfect! it makes much more sense now, thank you for your help!
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10/27/14

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