# Thread: Vectors on a plane

1. ## Vectors on a plane

Hi

I really need some assistance with the following problem:

"Find all unit vectors in the plane determined by u = (3,0,1) and v = (1,-1,1) that are perpendicular to the vector w = (1,2,0)".

The problem for me is that I donīt really know how to approach planes in general. For example, how do I calculate what plane is determined by the two vectors u and v?

What would u and v look like if they were serparate planes?

If someone know a website that explains the basics of vector planes I would appreciate the adress.

2. Bump

3. Originally Posted by Drdumbom
Bump
You waited less than 4 hours before a bump? People are not sitting waiting for you to post questions, you know! Some people only look in here every few days.

4. Originally Posted by Drdumbom
Hi

I really need some assistance with the following problem:

"Find all unit vectors in the plane determined by u = (3,0,1) and v = (1,-1,1) that are perpendicular to the vector w = (1,2,0)".

The problem for me is that I donīt really know how to approach planes in general. For example, how do I calculate what plane is determined by the two vectors u and v?
Use the cross product: the vector $\displaystyle \vec{u}\times \vec{v}$ is perpendicular to any linear combination of $\displaystyle \vec{u}$ and $\displaystyle \vec{v}$ and, so, is perpendicular to the entire plane. You need to find all unit vectors such that their dot product with that cross product and (1, 2, 0) is 0. That is, take (a, b, c) to be the vector. On condition is that $\displaystyle (a, b, c)\cdot(1, 2, 0)= a+ 2b= 0$. So you know that a= -2b.
Now do the same with (a, b, c) and $\displaystyle (3,0,1)\times (1,-1,1)$.

What would u and v look like if they were serparate planes?

If someone know a website that explains the basics of vector planes I would appreciate the adress.