They are written ( hk ! ), and denote the family of planes orthogonal to h \ mathbf { b _ 1 } + k \ mathbf { b _ 2 } + \ ell \ mathbf { b _ 3 }, where \ mathbf { b _ i } are the basis of the reciprocal lattice vectors . ( Note that the plane is not always orthogonal to the linear combination of direct lattice vectors h \ mathbf { a _ 1 } + k \ mathbf { a _ 2 } + \ ell \ mathbf { a _ 3 } because the reciprocal lattice vectors need not be mutually orthogonal . ) By convention, negative integers are written with a bar, as in for " 3.
