高中/数学/向量

向量

$$\vec {AB}=(x,y),\displaystyle |{\overrightarrow {AB}}|=\sqrt {x^2 + y^2}\\ \overrightarrow a \pm \overrightarrow b = ({x_1} \pm {x_2},{y_1} \pm {y_2})\\ \begin{aligned} \overrightarrow a \cdot \overrightarrow b &= {x_1}{x_2} + {y_1}{y_2}\\&=\left| {\overrightarrow a } \right| \cdot \left| {\overrightarrow b } \right| \cdot \cos \left\langle {\overrightarrow a ,\overrightarrow b } \right\rangle \\&=\left| {\overrightarrow a } \right| \cdot l_{a在b上的投影} \end{aligned}\\ \begin{aligned} \overrightarrow a \times \overrightarrow b &= {x_1}{y_2} - {x_2}{y_1}\\&=\left| {\overrightarrow a } \right| \cdot \left| {\overrightarrow b } \right| \cdot \sin \left\langle {\overrightarrow a ,\overrightarrow b } \right\rangle \\&=S_{平行四边形} \end{aligned}\\$$

奔驰定理