标签:rac 向量 com begin sqrt cos desc 叉积 amp
\[\vec a\times\vec b=|\vec a||\vec b|sin\theta\]
\[ \begin{eqnarray} sin\theta &= & \sqrt{1-cos^2\theta} \&=&\frac{\sqrt{(|\vec a|^2\cdot|\vec b|)^2-(\vec{a}\cdot{\vec{b})^2}}}{|\vec a||\vec b|} \\end{eqnarray} \]
\begin{eqnarray}
S &=& \sqrt{(|\vec a|^2\cdot|\vec b|)^2-(\vec{a}\cdot{\vec{b})^2}} \
&=& \sqrt{(x_1^2+y_1^2)(x_2^2+y_2^2)-(x_1x_2+y_1y_2)^2} \
&=& \sqrt{(x_1y_2)^2+(x_2y_1)^2-2x_1x_2y_1y_2} \
&=& \sqrt{(x_1y_2-x_2y_1)^2} \
&=& |x_1y_2-x_2y_1| \
\end{eqnarray}
标签:rac 向量 com begin sqrt cos desc 叉积 amp
原文地址:https://www.cnblogs.com/Vimin/p/11627515.html