Byron S. answered • 10/27/14

Math and Science Tutor with an Engineering Background

When two things intersect, their components are equal. You want to find where x

_{1}= x_{2}, y_{1}= y_{2}, and z_{1}= z_{2}This gives you a system of 3 equations, which you can use any two of to solve (If there is a solution. There's no guarantee that two lines will intersect! You'll have to check your results to make sure both lines completely meet.)

-2t = -9 + 5s

1 + 2t = 5s

3t = 2 + 4s

Adding the first two equations makes it easy to solve for

*s*.Byron S.

tutor

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

Dalia S.

10/27/14