4. Let $H$ be a point on the plane of $\triangle A B C$, and let $a, b, c, h$ represent the vectors $O A, O B, O C, O H$ respectively. If $\boldsymbol{a} \cdot \boldsymbol{b}+\boldsymbol{c} \cdot \boldsymbol{h}=\boldsymbol{b} \cdot \boldsymbol{c}+\boldsymbol{a} \cdot \boldsymbol{h}=\boldsymbol{c} \cdot \boldsymbol{a}+\boldsymbol{b} \cdot \boldsymbol{h}$, then $H$ is the ( ) of $\triangle A B C$.
(A) incenter
(B) circumcenter
(C) centroid
(D) orthocenter
4.D.

From $a \cdot b+c \cdot h=b \cdot c+a \cdot h$, we get $\boldsymbol{a} \cdot b+c \cdot h-b \cdot c-a \cdot h=0$, which is $(a-c) \cdot(b-h)=0$.
Therefore, $C A \cdot H B=0, H B \perp C A$.
Similarly, $\boldsymbol{H A} \perp \mathrm{BC}$.