Answer
$1$
Work Step by Step
$\nabla f=\biggl$
$v=\vec{PQ}=\vec{PO}+\vec{OQ}=\big<-2, -1, -1\big>+\big<0, -3, 5\big>=\big<-2, -4, 4\big>$
$\hat{v}=\biggl<-\dfrac{2}{6}, -\dfrac{4}{6}, \dfrac{4}{6}\biggr>$
Then,
$\nabla f_{(2, 1, 1)}=\biggl<1, 4, 6\biggr>$
Therefore,
$\mathbf{D_\hat{v}}f_{(2, 1, 1)}=\nabla f_{(2, 1, 1)}\cdot\hat{v}=-\dfrac{2}{6} -\dfrac{16}{6}+\dfrac{24}{6}=1$
