Unit translation vectors, bcc structure

[rayman123]

Homework Statement

Can someone please try to help me with this. I have a bcc structure and the question is ''Clearly indicate the unit translation vectors and state their value in Å.
I have attached the sketch :
http://img440.imageshack.us/img440/4879/picture3lh.jpg
are those t1,t2,t3 translation vectors?
I know the cell parameters are:$$a=b=c=31652\AA$$
Are these correct values of t1,t2,t3 then?
$$t_{1}=(-\frac{a}{2},\frac{a}{2},\frac{a}{2})=(-15826,15826,15826)\AA ?$$
and similarly the rest?

And one question more. We need to calculate the volume of the conventional unit cell and volume of the primitive unit cell, is this correct?
$$V_{conv}=a^{3}=3171\AA^{3}$$
$$V_{primitive}=\frac{V_{conv}}{2}}=1585.5\AA^{3}$$
Is the plane which has the highest degree of compaction (101)??
and the deree of compaction $$\frac{\sqrt{2}}{a^2}}$$?

Homework Equations

The Attempt at a Solution

 

[NateD]

The unit translation vectors are (t1, t2, t3) and they are equal to:t_{1}=\left(-\frac{a}{2},0,0\right)=(-15826, 0, 0)\AAt_{2}=\left(0,-\frac{a}{2},0\right)=(0, -15826, 0)\AAt_{3}=\left(0,0,-\frac{a}{2}\right)=(0, 0, -15826)\AAThe volume of the conventional unit cell is given by V_{conv}=a^{3}=3171\AA^{3}. The volume of the primitive unit cell is V_{primitive}=\frac{V_{conv}}{2}=1585.5\AA^{3}.The plane with the highest degree of compaction is the (101) plane and the degree of compaction is given by \frac{\sqrt{2}}{a^2}=0.04396.