问题
若向量 $\vec{a}$ $=$ $(x_{1}, y_{1})$, 向量 $\vec{b}$ $=$ $(x_{2}, y_{2})$, 向量 $\vec{i}$ 是 $x$ 轴上的单位向量，向量 $\vec{j}$ 是 $y$ 轴上的单位向量，则向量积 $\vec{a}$ $\times$ $\vec{b}$ $=$ $?$选项
[A]. $\vec{a}$ $\times$ $\vec{b}$ $=$ $\frac{(x_{1} \cdot x_{2})}{\mathbf{i}}$ $+$ $\frac{(y_{1} \cdot y_{2})}{\mathbf{j}}$[B]. $\vec{a}$ $\times$ $\vec{b}$ $=$ $(x_{1} \cdot x_{2}) + \mathbf{i}$ $+$ $(y_{1} \cdot y_{2}) + \mathbf{j}$
[C]. $\vec{a}$ $\times$ $\vec{b}$ $=$ $(x_{1} \cdot x_{2}) \mathbf{i}$ $+$ $(y_{1} \cdot y_{2}) \mathbf{j}$
[D]. $\vec{a}$ $\times$ $\vec{b}$ $=$ $(x_{1} \div x_{2}) \mathbf{i}$ $+$ $(y_{1} \div y_{2}) \mathbf{j}$
$\textcolor{red}{\vec{a}}$ $\textcolor{green}{\times}$ $\textcolor{red}{\vec{b}}$ $=$ $(\textcolor{orange}{x}_{\textcolor{cyan}{1}} \textcolor{green}{\cdot} \textcolor{orange}{x}_{\textcolor{cyan}{2}}) \mathbf{\textcolor{yellow}{i}}$ $\textcolor{green}{+}$ $(\textcolor{orange}{y}_{\textcolor{cyan}{1}} \textcolor{green}{\cdot} \textcolor{orange}{y}_{\textcolor{cyan}{2}}) \mathbf{\textcolor{yellow}{j}}$