  Here we show some results related with Kakeya conjecture which says that for
any integer $n\geq 2$, a set containing line segments in every dimension in
$\mathbb{R}^n$ has full Hausdorff dimension as well as box dimension. We proved
here that the Kakeya books, which are Kakeya sets with some restrictions on
positions of line segments have full box dimension. We also prove here a
relation between the projection property of Kakeya sets and the Kakeya
conjecture. If for any Kakeya set $K\subset\mathbb{R}^n$, the Hausdorff
dimension of orthogonal projections on $k\leq n$ subspaces is independent of
directions then the Kakeya conjecture is true. Moreover, the converse is also
true.
