1. ## Find a basis

I don't know why this one is giving me such a hard time but it is:

Find a basis for the set of vectors in R^3 in the plane x + 2y + z = 0

Thank you!

2. Hello
Originally Posted by baxyjr
I don't know why this one is giving me such a hard time but it is:

Find a basis for the set of vectors in R^3 in the plane x + 2y + z = 0
Any two vectors of the plane which don't share the same direction will give you a basis of this plane. To find two such vectors one can pick up three points $\displaystyle A$, $\displaystyle B$ and $\displaystyle C$ on the plane and check that $\displaystyle \vec{AB} \nparallel \vec{BC}$.

3. Originally Posted by flyingsquirrel
Hello

Any two vectors of the plane which don't share the same direction will give you a basis of this plane. To find two such vectors one can pick up three points $\displaystyle A$, $\displaystyle B$ and $\displaystyle C$ on the plane and check that $\displaystyle \vec{AB} \nparallel \vec{BC}$.
Thank you!

Ok, I think I get it.

So you're saying that as long as I pick two vectors in R3 that are linearly independent and satisfy the equation, that I am good?

Thank god for this site! Especially when you are taking a class that normally covers 4 months in four weeks!

4. Originally Posted by baxyjr
Thank you!

Ok, I think I get it.

So you're saying that as long as I pick two vectors in R3 that are linearly independent and satisfy the equation, that I am good?
Yes. The plane will be a vector space of dimension 2, so any two linearly independent vectors in it will form a basis.