# Crystal plane perpendicularity to direction

1. Sep 6, 2012

### dikmikkel

1. The problem statement, all variables and given/known data
Show that the direction [hkl] is perpendicular to the plane (hkl) in a cubic system.

2. Relevant equations
None, maybe cross product

3. The attempt at a solution
I've tried to define the crystal translation vectors(cubic means a=b=c):
$\vec{a}_1 = a\hat{x}\\ \vec{a}_2 = a\hat{y}\\ \vec{a}_3 = a\hat{z}$
I just can't imagine how to obtain the vector normal to the plane. I cannot use the reciprocal space as we haven't gone over that yet. Please help me, it is not to be handed in i just need to understand it.

My question is: What is the connection between Miller Indicies of a plane and the plane's normal vector.