Find a perpendicular foot and use it as a triangle height

Referred to the origin $O$, points $A$ and $B$ have position vectors $\mathbf a=-\mathbf i-6\mathbf j-5\mathbf k$ and $\mathbf b=4\mathbf i+4\mathbf j+10\mathbf k$ respectively. Point $P$ lies on $AB$, between $A$ and $B$, such that $AP:PB=2:3$.

(i) Find the position vector $\overrightarrow{OP}$.

(ii) Show that $\overrightarrow{AB}$ and $\overrightarrow{OP}$ are perpendicular.

The vector $\mathbf c$ is a unit vector in the direction of $\overrightarrow{OP}$.

(iii) Find the value of $|\mathbf a\cdot\mathbf c|$ and give the geometrical interpretation of $|\mathbf a\cdot\mathbf c|$. Hence, or otherwise, find the area of triangle $OAB$.