What is the value of k in this equation?

[Alexandra7]

http://ca.answers.yahoo.com/question/index?qid=20131027134934AAQQUWp

I really need help. All the information is on that link.

I've spent 30 minutes or so trying to figure this out but I can't and I'm starting to get really upset.

If you guys can find the value of k, I can take it from there. I just have no idea how to find k and it's stressing me out so much.

 

[Simon Bridge]

Welcome to PF;

Find the value of k such that three planes will not intersect at a single point??

X +2y -Z-5=0

X + ky -3z +11=0

2x + y + z + 10 = 0

I have no idea how to find the value of k :(

... is there a special meaning for the capitalization?
Assuming none:

Consider the two planes that do not have k in them - they must intersect along a line right?
What does the third plane have to avoid doing to make all three intersect at a point?

 

[Alexandra7]

Welcome to PF;
... is there a special meaning for the capitalization?
Assuming none:

Consider the two planes that do not have k in them - they must intersect along a line right?
What does the third plane have to avoid doing to make all three intersect at a point?

No, no meaning for caps.

I actually did consider them. My problem is, what do I do with that idea? How do I solve k based on that? Like I've tried everything and I'm just about to break because I need to know this. My teacher has never given us a question like this so I feel rather hopeless as much as I love this course.

 

[Alexandra7]

Welcome to PF;
... is there a special meaning for the capitalization?
Assuming none:

Consider the two planes that do not have k in them - they must intersect along a line right?
What does the third plane have to avoid doing to make all three intersect at a point?

Oh and all three planes when using n1 x n2 • n3 must equal 0 and be coplanar. If it does not equal 0, then it intersects at a single point. Again, I just don't know how to find K. I've tried dot product, linear equations, etc

 

[Simon Bridge]

... think geometry not algebra!
Start the algebra once you know what you are aiming for.

In general, three planes will have an intersection at a point. i.e. there is one point that is on all three planes.
But they don't have to. They actually don't have to intersect at all.

Two planes will intersect on a line - with three planes there will be 2 or three lines of intersection (where one plane intersects with one of the others).

In your problem you have two planes that intersect (in a line) so you can't do anything about that.

You have a third plane whose orientation you get to change by changing the variable k.

You have to use your imagination - or get some bits of stiff card and hold them up at different angles.

[edit: and try not to get impatient - I'm typing as fast as I can :( ]

 

[Alexandra7]

... think geometry not algebra!
Start the algebra once you know what you are aiming for.

In general, three planes will have an intersection at a point. i.e. there is one point that is on all three planes.
But they don't have to. They actually don't have to intersect at all.

Two planes will intersect on a line - with three planes there will be 2 or three lines of intersection (where one plane intersects with one of the others).

In your problem you have two planes that intersect (in a line) so you can't do anything about that.

You have a third plane whose orientation you get to change by changing the variable k.

You have to use your imagination - or get some bits of stiff card and hold them up at different angles.

[edit: and try not to get impatient - I'm typing as fast as I can :( ]

Only problem is, I've only been taught to solve with algebra. It tried putting x=0 and solve for x, z = 0 and solve for z, then sub in x and z into equation 2 and try to solve for k, but it's no good!

 

[Simon Bridge]

Only problem is, I've only been taught to solve with algebra.

Do you not know what a plane looks like?
Can you not imagine a couple of planes in space?
If you do not, and cannot, I cannot help you.

You have to know what the equations mean!

 

[Alexandra7]

Do you not know what a plane looks like?
Can you not imagine a couple of planes in space?
If you do not, and cannot, I cannot help you.

You have to know what the equations mean!

I figured it out. K=4

Thanks for your help, I guess..

 

[nasu]

You have to know what the equations mean!

It looks like all she cares about is the answer. It does not matter what this means.

 

[Simon Bridge]

I figured it out. K=4

That's great!
Do you know why k=4?

Thanks for your help, I guess..

I never even got that far because you indicated you didn't want to go there.

You understand that we cannot do your homework for you?
Instead we have to sort-of nudge you onto the right track.

Good luck.