本文详细介绍了四种叉乘计算公式的几何推导方法，包括旋转法、三角形面积分解法、平行四边形法和三角形拼接法，最终得出面积表达式x2y1-x1y2。
叉乘计算公式几何推导
推导方法1
经过旋转变换之后，对象的面积是不会改变的。
把△FEG\triangle{FEG}△FEG旋转θ\thetaθ到△F′EG′\triangle{F'EG'}△F′EG′
△F′EG′\triangle{F'EG'}△F′EG′的面积计算是简单的，即F’的纵坐标 乘以G’的横坐标
首先计算出F’ G’的坐标
F′(x,y)=[x1y1][cos(θ)−sin(θ)sin(θ)cos(θ)]=[x1cos(θ)+y1sin(θ)−x1sin(θ)+y1cos(θ)] F'(x, y) = \left[\begin{matrix}x_{1} & y_{1}\end{matrix}\right] \left[\begin{matrix}\cos{\left (\theta \right )} & - \sin{\left (\theta \right )}\\\sin{\left (\theta \right )} & \cos{\left (\theta \right )}\end{matrix}\right] = \left[\begin{matrix}x_{1} \cos{\left (\theta \right )} + y_{1} \sin{\left (\theta \right )} & - x_{1} \sin{\left (\theta \right )} + y_{1} \cos{\left (\theta \right )}\end{matrix}\right] F′(x,y)=[x1y1][cos(θ)sin(θ)−sin(θ)cos(θ)]=[x1cos(θ)+y1sin(θ)−x1sin(θ)+y1cos(θ)]
G′(x,y)=[x2y2][cos(θ)−sin(θ)sin(θ)cos(θ)]=[x2cos(θ)+y2sin(θ)−x2sin(θ)+y2cos(θ)] G'(x, y) = \left[\begin{matrix}x_{2} & y_{2}\end{matrix}\right] \left[\begin{matrix}\cos{\left (\theta \right )} & - \sin{\left (\theta \right )}\\\sin{\left (\theta \right )} & \cos{\left (\theta \right )}\end{matrix}\right] = \left[\begin{matrix}x_{2} \cos{\left (\theta \right )} + y_{2} \sin{\left (\theta \right )} & - x_{2} \sin{\left (\theta \right )} + y_{2} \cos{\left (\theta \right )}\end{matrix}\right] G′(x,y)=[x2y2][cos(θ)sin(θ)−sin(θ)cos(θ)]=[x2cos(θ)+y2sin(θ)
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