<p>I'm trying to understand basis vectors and the plane equation and I am confused. From what I saw, if we take a basis vector i, j, k, each variable point to the axe (x, y, z). Are i,j,k scalars or vectors? It seems that any vector can be seen as i<em>x, j</em>y, k*z. Does that mean that changing the values of i,j,k can "rotate" the whole plane (the world)? Does this has any connection with the plane equation? Maybe that I am mixing things up.</p>

CC BY-SA 3.0
2017-09-13T04:42:12.373Z
You should probably include what your using as reference as its hard to tell.
joojaa
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2017-09-13T12:38:58.807Z
In my experience, i,j,k typically imply mutually orthogonal unit *vectors*.
Simon F
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2017-09-13T13:09:51.340Z
@SimonF they do not have to be though there areplenty of reasons to transform them.
joojaa
CC BY-SA 3.0
2017-09-14T23:18:29.780Z
I am thinking mainly about 3d space for games. I have the feeling that the basis vectors are the vectors which show the orientation of the space. On wikipedia, the 2 images on the right seems to show this. But still, I am not sure that it is the main purpose of basis vectors. Also, does orthogonal mean at 90 degrees? As an example, in 2d, does (1,0) and (0,1) are orthogonals? And (0.7, 0) and (0, 1) are not? The wiki page : https://en.wikipedia.org/wiki/Basis_(linear_algebra)
Choz
<vectors>
Basis vectors and plane equation
Choz
# Basis vectors and plane equation

(Asked by: username_0 on 2017-09-12)

I'm trying to understand basis vectors and the plane equation and I am confused. From what I saw, if we take a basis vector i, j, k, each variable point to the axe (x, y, z). Are i,j,k scalars or vectors? It seems that any vector can be seen as i*x, j*y, k\*z. Does that mean that changing the values of i,j,k can "rotate" the whole plane (the world)? Does this has any connection with the plane equation? Maybe that I am mixing things up.

**Tags:** vectors

> **Comments:**
> **username_1**: You should probably include what your using as reference as its hard to tell.  
> **username_2**: In my experience, i,j,k typically imply mutually orthogonal unit *vectors*.  
> **username_1**: @username_2 they do not have to be though there areplenty of reasons to transform them.  
> **username_0**: I am thinking mainly about 3d space for games. I have the feeling that the basis vectors are the vectors which show the orientation of the space. On wikipedia, the 2 images on the right seems to show this. But still, I am not sure that it is the main purpose of basis vectors. Also, does orthogonal mean at 90 degrees? As an example, in 2d, does (1,0) and (0,1) are orthogonals? And (0.7, 0) and (0, 1) are not? The wiki page : https://en.wikipedia.org/wiki/Basis_(linear_algebra)  

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## 0 answers

