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:

\(\overrightarrow u .\overrightarrow v \)

\(\left[ {\overrightarrow u .\overrightarrow v } \right]\)

\(\left[ {\overrightarrow u ,\overrightarrow v } \right]\)

\(\left[ {\overrightarrow v ,\overrightarrow u } \right]\)

\(\left( {{y_1}{z_2} - {y_2}{z_1};{z_1}{x_2} - {z_2}{x_1};{x_1}{y_2} - {x_2}{y_1}} \right)\)

\(\left( {{x_1}{y_2} - {x_2}{y_1};{y_1}{z_2} - {y_2}{z_1};{z_1}{x_2} - {z_2}{x_1}} \right)\)

\(\left( {{z_1}{x_2} - {z_2}{x_1};{y_1}{z_2} - {y_2}{z_1};{x_1}{y_2} - {x_2}{y_1}} \right)\)

\(\left( {{x_1}{y_2} - {x_2}{y_1};{z_1}{x_2} - {z_2}{x_1};{y_1}{z_2} - {y_2}{z_1}} \right)\)

\(\left( {1;0;0} \right)\)           

\(\left( {0;0;6} \right)\)           

\(\left( { - 6;0;0} \right)\)

\(\left( {0;0; - 6} \right)\)

\(\overrightarrow u .\overrightarrow v  = 0\)

\(\overrightarrow u .\overrightarrow w  = 0\)

\(\left[ {\overrightarrow u ,\overrightarrow w } \right] = 0\)        

\(\left[ {\overrightarrow v ,\overrightarrow w } \right] = 0\)

\(\left( {5;2; - 3} \right)\)        

\(\left( { - 5;2; - 3} \right)\)    

\(\left( { - 5; - 2; - 3} \right)\)

\(\left( { - 5; - 2;3} \right)\)

\(\left[ {\overrightarrow u ,\overrightarrow v } \right] = 0\)

\(\left[ {\overrightarrow u ,\overrightarrow v } \right] = \overrightarrow 0 \)    

\(\left[ {\overrightarrow u ,\overrightarrow v } \right] = k\)         

\(k\left[ {\overrightarrow u ,\overrightarrow v } \right] = 0\)

\(12\)

\(0\)

\(\left( {2;8;2} \right)\)           

\(\left( {0;0;0} \right)\)