- #1

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L2: r(t) = (3 + 4t)i + (4 - 8t)j

I know that they are perfendicular but how do I go about finding the point of intersection?

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- Thread starter lwelch70
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- #1

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L2: r(t) = (3 + 4t)i + (4 - 8t)j

I know that they are perfendicular but how do I go about finding the point of intersection?

- #2

Mark44

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- #3

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I'm sorry but could you walk me through this step?

- #4

Mark44

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L2: r

While we're at it let's give different names to the two functions so we can tell them apart.

For each value of s, r

Similarly, for each value of t, r

At any point of intersection the coordinates of the point on L1 have to be equal to the coordinates of the point on L2.

- #5

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L2: r_{2}(s) = (3 + 4s)i + (4 - 8s)j

While we're at it let's give different names to the two functions so we can tell them apart.

For each value of s, r_{2}(s) gives you a different vector. This vector extends from the origin to a point in the plane. What are the coordinates of that point?

Similarly, for each value of t, r_{1}(t) likewise gives you a different vector. This vector extends from the origin to a point in the plane. What are the coordinates of that point?

At any point of intersection the coordinates of the point on L1 have to be equal to the coordinates of the point on L2.

So I've been trying to set the i value of L1 to theat of L2 and likewise for the j value. I can't seem to get the answers though. I solve for the variable (in L1's case "T", correct?).

- #6

Mark44

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What did you get?

- #7

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t=-4 for i and t=-1/9 for j

- #8

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Anyone else have any help???

- #9

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Show your work for solving for t and s and we can see where you went astray.

- #10

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Show your work for solving for t and s and we can see where you went astray.

-5+2t=3+4t

solved for t to equal -4

5+t=4-8t

solved for t to equal -1/9

I'm not really sure if I went about that right but I'm stuck.

- #11

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- #12

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I set the second set with an "s"

-5+2t = 3+4s

solved for s = -2+(1/2)t

Do I then plug that in for the s in the original to solve?

- #13

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Once you get s and t figured out you can plug them in their equations to check they are at the same point. I assume you can take it from here.

- #14

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- #15

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