  In this paper, we define a differential operator as a modified Dirac
operator. Using the operator, we introduce a quaternionic $k$-vector field on a
quaternionic K\"{a}hler manifold and show that any quaternionic $k$-vector
field corresponds to a holomorphic $k$-vector field on the twistor space. We
calculate the dimension of the space of quaternionic $k$-vector fields on
$\mathbb{H}P^n$.
