In the paper the geometric properties of the positive cone and positive part of the unit ball of the space of operator-valued continuous space are discussed. In particular we show that $\text{ext-ray}{\text{C}}_{+}(K,ℒ\left(H\right))=\{{ℝ}_{+}{\mathbf{1}}_{\left\{k_0\right\}}𝐱\otimes 𝐱:𝐱\in 𝐒\left(H\right),k_0\text{is}\text{an}\text{isolated}\text{point}\text{of}K\}$$\text{ext}{𝐁}_{+}...$