Linear alg. Who is really smart here and can solve this?

[cleopatra]

Homework Statement

1) x=3+t
y=2-4t
z=-5+11t

2)12x+10y-4z=46

Find the point where these two lines intersect.

12x+10*0-4*0=46
x=3,8...

doesn´t make any sense

Homework Equations

The Attempt at a Solution

 

[gabbagabbahey]

Homework Statement

1) x=3+t
y=2-4t
z=-5+11t

2)12x+10y-4z=46

Find the point where these two lines intersect.

12x+10*0-4*0=46
x=3,8...

doesn´t make any sense

For starters, you don't have two intersecting lines...2) is the equation of a plane, not a line.

Secondly, you are right: what you did doesn't make any sense...why have you assumed that y=z=0 at the point of intersection?

Just plug your parametric equations for x,y, and z into the equation of the plane and solve for t...what does that value of t make x,y and z?

 

[Dick]

For starters, you don't have two intersecting lines...2) is the equation of a plane, not a line.

Secondly, you are right: what you did doesn't make any sense...why have you assumed that y=z=0 at the point of intersection?

Just plug your parametric equations for x,y, and z into the equation of the plane and solve for t...what does that value of t make x,y and z?

cleopatra has already been told to do this twice on the other thread dedicated to this problem.

 

[gabbagabbahey]

cleopatra has already been told to do this twice on the other thread dedicated to this problem.

hmmm...yes, I see...

Cleopatra, we are not here to do your homework for you, you need to show some attempt at a solution.

And creating multiple threads for the same topic is against forum rules.

 

[cleopatra]

36+12t+20-40t+20-44t=46
t=30/76


?

 

[CompuChip]

First of all let's be clear on the question.
Does it really say "find the point where these two lines intersect"?
Because I definitely get a line of intersection.

 

[cleopatra]

yes it says "point". That´s why it confuses me as well.

 

[Dick]

36+12t+20-40t+20-44t=46
t=30/76?

There you go. Well done. Now you can use your value of t to find x, y and z.
Ooops. Wait a minute. t isn't 30/76. Check your arithmetic.

 

[gabbagabbahey]

36+12t+20-40t+20-44t=46
t=30/76


?

Careful; 44+40-12=72 not 76

 

[gabbagabbahey]

First of all let's be clear on the question.
Does it really say "find the point where these two lines intersect"?
Because I definitely get a line of intersection.

You might want to recheck your calculation then

 

[Dick]

First of all let's be clear on the question.
Does it really say "find the point where these two lines intersect"?
Because I definitely get a line of intersection.

How do you figure? Do you mean the line lies in the plane? I don't think so.

 

[gabbagabbahey]

yes it says "point". That´s why it confuses me as well.

Why does this confuse you?

Imagine a sheet of paper as the plane, and your pencil as the line...if you lie your pencil flat on the paper, then the intersection is the entire line, but if you just poke a whole through the piece of paper and slide your pencil part way through it, the intersection is just a point...you can also make it so the two don't intersect at all by holding the pencil a few inches above the paper.

In this case, the line and the plane intersect at a point.