Cho ba véc tơ \(\overrightarrow {{u_1}} ,\overrightarrow {{u_2}} ,\overrightarrow {{u_3}} \) thỏa mãn \(\left[ {\overrightarrow {{u_1}} ;\overrightarrow {{u_2}} } \right].\overrightarrow {{u_3}}  = 0\). Khi đó ba véc tơ đó:

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

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

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

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

\(\overrightarrow 0 \)            

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

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

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

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

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

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

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

\(\overrightarrow {{u_1}} .\overrightarrow {{u_2}}  = 0\)

\(\overrightarrow {{u_1}} .\overrightarrow {{u_2}}  = \overrightarrow 0 \)       

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

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

\(b = 2c\)

\(c = 2b\)

\(b =  - 2c\)

\(b = c\)

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

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

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

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