# Units Vectors and Planes

1. Apr 4, 2007

### kskiraly

1. The problem statement, all variables and given/known data

Find 2 unit vectors u1, u2, lying in the plane, x-y+z=0, which are not parallel to each other.

3. The attempt at a solution

I've tried taking the unit vector of the normal vector <1,-1,1> which is <1/rad(3),-1/rad(3),1/rad(3)>, but my teacher has told me it is not in the plane.

Then for my second vector, I created a parallel vector, but then I reread the question and found out they are not supposed to be parallel.

2. Apr 4, 2007

### HallsofIvy

Staff Emeritus
Yes, obviously. x- y+ z= (1-(-1)+ 1)/rad(3)= rad(3) not 0! You are aware, I am sure, that the normal vector to a plane is not in the plane! (If you are not, reread the definition of "normal vector".)

A very good case for always rereading the question (several times)! Yes, it says "not parallel".

To find a vector in the plane x- y+ z= 0, look for values of x, y, z that satisfy that equation. There are, of course, an infinite number of such choices. You can choose any values you like for x and y, for example, and then solve the equation for z. 1 and 0 are good, simple, choices.
If x= 1 and y= 0, then z must satisfy 1- 0+ z= 0.
If x= 0 and y= 1, then z must satisfy 0- 1+ z= 0.

Now form unit vectors from <x, y, z> and show that they are not parallel.