Understanding Dot Product for Diffraction Peaks Calculation

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Homework Statement



It is question number 1a here:

http://web.utk.edu/~tbarnes/website/cm/cm_hw/hw4/cm_hw4.pdf

The Attempt at a Solution



I'm not entirely sure how to go about this. I've rearranged this equation to get

-3ln(0.33)=Ghkl2<\delta^2>The thing that confuses me is that Ghkl2 is a vector quantity, right? In this case, since we are talking about the (800) plane, would this be just the dot product of G with itself (64)? I'm just not sure how I'm supposed to turn this into a scalar. Any help would be greatly appreciated.
 
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Please recheck your definition of the dot product.
 

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