# Thread: Calc 3 Help. Finding point of intersection of 2 lines

1. ## Calc 3 Help. Finding point of intersection of 2 lines

Hi,
So the problem states that there are two lines

L1 : x=12+3t, y=5+3t, z=5+t
L2 : x=-5+4t, y=-14+5t z=-6+4t

i've already tried setting the x's, y's, and z's equaling each other.
i can't seem to find another way to find the point of intersection.
Any help would be greatly appreciated. thanks you.

2. Originally Posted by jeugenej1
Hi,
So the problem states that there are two lines

L1 : x=12+3t, y=5+3t, z=5+t
L2 : x=-5+4t, y=-14+5t z=-6+4t

i've already tried setting the x's, y's, and z's equaling each other.
i can't seem to find another way to find the point of intersection.
Any help would be greatly appreciated. thanks you.
The problem is that the same parameter is being used in both equations. They should have ben written:

L1 : x=12+3t, y=5+3t, z=5+t
L2 : x=-5+4s, y=-14+5s z=-6+4s

Now equate:

12 + 3t = 5 + 4s .... (1)

5 + 3t = -14 + 5s .... (2)

5 + t = -6 + 4s .... (3)

Solve two of these equations simultaneously and check that the solution satisfies the third.

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