Byron S. answered • 10/27/14
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Math and Science Tutor with an Engineering Background
When two things intersect, their components are equal. You want to find where x1 = x2, y1 = y2, and z1 = z2
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.
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