Sin của góc giữa hai véc tơ $\overrightarrow {{u_1}} ,\overrightarrow {{u_2}}$ là:

$\overrightarrow u  = \left( {\left| {\begin{array}{*{20}{c}}\begin{array}{l}{y_2}\\{y_1}\end{array}&\begin{array}{l}{z_2}\\{z_1}\end{array}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}\begin{array}{l}{z_2}\\{z_1}\end{array}&\begin{array}{l}{x_2}\\{x_1}\end{array}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}\begin{array}{l}{x_2}\\{x_1}\end{array}&\begin{array}{l}{y_2}\\{y_1}\end{array}\end{array}} \right|} \right)$                      

$\overrightarrow u  = \left( {\left| {\begin{array}{*{20}{c}}\begin{array}{l}{x_1}\\{x_2}\end{array}&\begin{array}{l}{y_1}\\{y_2}\end{array}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}\begin{array}{l}{y_1}\\{y_2}\end{array}&\begin{array}{l}{z_1}\\{z_2}\end{array}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}\begin{array}{l}{z_1}\\{z_2}\end{array}&\begin{array}{l}{x_1}\\{x_2}\end{array}\end{array}} \right|} \right)$

$\overrightarrow u  = \left( {\left| {\begin{array}{*{20}{c}}\begin{array}{l}{y_1}\\{y_2}\end{array}&\begin{array}{l}{z_1}\\{z_2}\end{array}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}\begin{array}{l}{z_1}\\{z_2}\end{array}&\begin{array}{l}{x_1}\\{x_2}\end{array}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}\begin{array}{l}{x_1}\\{x_2}\end{array}&\begin{array}{l}{y_1}\\{y_2}\end{array}\end{array}} \right|} \right)$          

$\overrightarrow u  = \left( {\left| {\begin{array}{*{20}{c}}\begin{array}{l}{z_1}\\{z_2}\end{array}&\begin{array}{l}{x_1}\\{x_2}\end{array}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}\begin{array}{l}{x_1}\\{x_2}\end{array}&\begin{array}{l}{y_1}\\{y_2}\end{array}\end{array}} \right|;\left| {\begin{array}{*{20}{c}}\begin{array}{l}{y_1}\\{y_2}\end{array}&\begin{array}{l}{z_1}\\{z_2}\end{array}\end{array}} \right|} \right)$

$\overrightarrow 0$            

$\left( { - 2; - 1; - 1} \right)$

$\left( {2;1;1} \right)$

$\left( { - 1; - 2; - 1} \right)$

$\left[ {\overrightarrow {{u_1}} ,\overrightarrow {{u_2}} } \right] = \left[ {\overrightarrow {{u_2}} ,\overrightarrow {{u_1}} } \right]$                         

$\left[ {\overrightarrow {{u_1}} ,\overrightarrow {{u_2}} } \right] =  - \left[ {\overrightarrow {{u_2}} ,\overrightarrow {{u_1}} } \right]$

$\left[ {\overrightarrow {{u_1}} ,\overrightarrow {{u_2}} } \right] - \left[ {\overrightarrow {{u_2}} ,\overrightarrow {{u_1}} } \right] = \overrightarrow 0$  

$\left[ {\overrightarrow {{u_1}} ,\overrightarrow {{u_2}} } \right] + \left[ {\overrightarrow {{u_2}} ,\overrightarrow {{u_1}} } \right] = 0$

$\overrightarrow {{u_1}} .\overrightarrow {{u_2}}  = 0$

$\overrightarrow {{u_1}} .\overrightarrow {{u_2}}  = \overrightarrow 0$       

$\left[ {\overrightarrow {{u_1}} ,\overrightarrow {{u_2}} } \right] = \overrightarrow 0$        

$\left[ {\overrightarrow {{u_1}} ,\overrightarrow {{u_2}} } \right] = 0$

$b = 2c$

$c = 2b$

$b =  - 2c$

$b = c$

$\left[ {\overrightarrow {{u_1}} ;\overrightarrow {{u_2}} } \right].\overrightarrow {{u_1}}  = 0$      

$\left[ {\overrightarrow {{u_1}} ;\overrightarrow {{u_2}} } \right].\overrightarrow {{u_2}}  = \overrightarrow 0$          

$\left[ {\overrightarrow {{u_1}} ;\overrightarrow {{u_2}} } \right].\overrightarrow {{u_2}}  = 0$      

$\left[ {\overrightarrow {{u_1}} ;\overrightarrow {{u_2}} } \right] \bot \overrightarrow {{u_1}}$ 

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