Question

I'm trying to find the intersection of two parametric lines and need help

Answer 1

\[L1: x=1-2t y=-1-4t z=-2+t\]
\[L2: -3+t y=-2+3t z=3-t\]

Answer 2

woops, I should have done those better

Answer 3

I first tried setting all of these equal to t and then just setting them equal to eachother and that didn't work

Answer 4

I got (7, 20/3, -7) and I guess that's wrong

Answer 5

Try setting the x values of line one equal to the x values of the line two. Then do the same for the y values and the z values. For each of the t values obtained ( one for each of the equations x=x y=y z=z) you will need to plug those values in for t in those equations for the value.

Does this help?

Answer 6

so like in the first one I'd have 1-2t=-3+t I'd solve for t, then plug that value into one of the original equations?

Answer 7

Into the equation for x yes. Then you do the same for y and for z.

Answer 8

Hey, I'm sorry I was thinking about a different method. You had me confused with you variables.
First thing first, you need to change t to s in your second line because the parameters are separate.

Answer 9

Sorry if I am confusing you. You would need to do:

1-2t=-3+s for x=x now you need one for y=y then solve the system for s and t. Then set z=z to verify that the equations are intersecting lines.

Answer 10

If z=z at the end once you plug in the values for s and t obtained from solving the two equations x=x and y=y you have an intersecting line! Then you can choose either s or t and plug that value in to the original equation (choose t for line 1 and s for line two) it does not matter which you chose (s or t) they yield the same result.

Answer 11

Since I have done x=x, what would you get for y=y?

Answer 12

-1-4t=-2+5s

Answer 13

Cool, then you'd solve for the system s+2t=4 and 5s+4t=-6

Answer 14

L1: Y=-1-4t
L2: Y=-2+3s

y=y:
-1-4t=-2+3s

I think you may have mistakenly used 5 instead of 3?

Answer 15

yes! I did

Answer 16

glad you caught that before I got very far, haha

Answer 17

-1-4t=-2+3s
1-2t==3+s

These are the two equations i have found, just solve for s and t. then set z=z and check if z does equal z when you put those values in. If it does the lines intersect and you can solve for the point of intersection.

Answer 18

I got t=9 and s=-14 and that doesn't check out :(

Answer 19

I rearranged the equations:

-4t-3s=-1
-2t-s=2

When I solved I got:

s=5
t=-3.5

Answer 20

Whoops! I was wrong, Sorry Doing this with out a calculator!

Answer 21

so then you would plug that value in for t in one of the original equations?

Answer 22

it's fine, I'll do the math again anyways

Answer 23

Yes precisely.

Answer 24

okay, awesome. Thank you for your help :)

Answer 25

Yep! Sorry for being so discombobulated! :)

Answer 26

hahaha, you're not the only one! Turns out I didn't even give the correct original equations :P