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d=2[itex]\pi[/itex]/lGl

where G is the reciprocal lattice vector:

G=hb1+kb2+kb3

Somehow I can't get this formula to work. I wonna calculate the distance between (200) planes. This should be a/2, where a is the lattice constant. But (look it up) b1=2[itex]\pi[/itex]/a (-x + y +z), where x, y and z are unit vectors. And so G= hb1 = 2[itex]\pi[/itex]/a (-x + y +z) and thus lGl = h2[itex]\pi[/itex]/a * √3

=>

d= a/(2√3)

But this can't be right. I have no idea why I get that factor of √3, because I checked everything. Where did I make a silly mistake?