Solving a Tutorial Problem on Bravais Lattice

[retupmoc]

Im a bit stuck on this tutorial problem on Bravais Lattices. The question initially asks to sketch the 5 2D Bravais lattices which i have done but i have no idea how to proceed with the next part, The question states

" use the definition of the Bravais lattice to show that the third real space axis is normal to the plane"

I assume somewhere i have to use the cross-product but i don't know at what point or even how in this case.
For exampe for the c-a plane of the primitive monoclinc the only info i know is that the length c does not equal that of a and that they are not normal. How do i proceed?

Thanks

 

[StatusX]

I don't understand the question. Are you supposed to assume that a 3D bravais lattice has one of these as a cross section, and that then the third lattice vector must be normal to these planes? Because that is not, in general, true. Look at the body centered cubic lattice with the (100) planes.