Need help to start

[Hira Javaid]

Can someone give me a hint to start it please
Find two non-zero vectors u and v in R3 such that {s u+ t v | s, t ∈ R} is a line in R3.

 

[Dr.Peterson]

Can someone give me a hint to start it please
Find two non-zero vectors u and v in R3 such that {s u+ t v | s, t ∈ R} is a line in R3.

The first step is to do something -- anything!

Try this: What will go wrong if you just pick any two arbitrary vectors u and v?

Then, what might you do to fix that?

 

[HallsofIvy]

Since su+ tv has two variables, as long as u and v are independent, that will be two dimentional, a plane rather than a line. Do you know what "independent" and "dependent" vectors are?

 

[Hira Javaid]

Yes

Since su+ tv has two variables, as long as u and v are independent, that will be two dimentional, a plane rather than a line. Do you know what "independent" and "dependent" vectors are?

Yes i know

 

[Hira Javaid]

The first step is to do something -- anything!

Try this: What will go wrong if you just pick any two arbitrary vectors u and v?

Then, what might you do to fix that?

We will take linear combination of that vectors..but whats next..and how can i prove that they are in line

 

[Hira Javaid]

Since su+ tv has two variables, as long as u and v are independent, that will be two dimentional, a plane rather than a line. Do you know what "independent" and "dependent" vectors are?

I still don't understood what to do exactly if i can take any two supposed vector and write it in linear combination what will be next like what's the major thing which i need to do..can you please explain that

 

[HallsofIvy]

You did not answer the question that you quoted! Do you know what "independent" and "dependent" vectors are?

If a and b can be any numbers what is a<1, 0>+ b<0, 1>? What is a<1, 0>+ b<2, 0>?

 

[Dr.Peterson]

I still don't understood what to do exactly if i can take any two supposed vector and write it in linear combination what will be next like what's the major thing which i need to do..can you please explain that

The next thing to do is to think about what you are being told! Don't act helpless.

What is the set of all linear combinations of two independent vectors? What is different if they are not independent?

We will take linear combination of that vectors..but whats next..and how can i prove that they are in line

Your goal is not to prove that the set will always form a line, but to find some vectors for which it is not.

 

[pka]

Two vectors [imath]\vec{U}~\&~\vec{V}[/imath]are colinear if and only if they are non-zero scalar multiples of each other.