Question

So I have two lines and their equations, I know they intersect in a point A. I need to find the coordinates

Answer 1

r1= (10 6 -1) + s(2 -5 -2)
r2= (2 1 -3) + t(3 5 2)

Answer 2

So r1=r2, but I am having problems with solving it

Answer 3

I got you solution ;)

Just hold on.

Answer 4

What I did:
10 + 2s= 2 + 3t
6-5s = 1 +5t
-1-2s=-3+2t

So I added 1 and 3 and got: 9=-1 + 5t
So t=10

And with that I get that s= -9

But it is not working for the first equation

Answer 5

Ok...and why isn't my method working?

Answer 6

I can put step by step of what I did if you want

Answer 7

The problem is that I am not sure I should use reduce form

Answer 8

It's better use reduce form. I'll see what you did.

Answer 9

Thanks

Answer 10

I think I did a dumb error...give me a sec

Answer 11

Ok...if I add 1 and 3 I get

9=5t-1
So t=2

If I substitute t in eq 2 I get
6-5s=1+10
-5s=5
s=-1

Answer 12

Ops, i find an error here.

\[r_1\]
\[x=10+2s\]\[y=6-5s\]\[z=-1-2s\]
\[r_2\]
\[x=2+3t\]\[y=1+5t\]\[z=-3+2t\]

chose 2 equation

\[10+2s=2+3t\]\[6-5s=1+5t\]
\[t=2~~and~~s=-1\]

now replace this values

\[r_1\]
\[x=10+2*(-1)\]\[y=6-5*(-1)\]\[z=-1-2*(-1)\]
\[r_2\]
\[x=2+3*2\]\[y=1+5*2\]\[z=-3+2*2\]

then we have

\[r_1\]
\[x=8\]\[y=11\]\[z=1\]
\[r_2\]
\[x=8\]\[y=11\]\[z=1\]

Answer 13

And that gives (8 11 1) which seems correct for both...but it is different

Answer 14

oh...same result :D

Answer 15

Yeah ;)

Answer 16

why was your answer different? (the first one)

Answer 17

I don't know, I guess that I'm made some mistake.

Answer 18

ok :) my mistake was really silly...thanks a lot

Answer 19

You're welcome