\(\eqalign{ & a)\overrightarrow u = (1;2; – 3),\overrightarrow v = ( – 4;1;2); \cr & b)\overrightarrow u = 3\overrightarrow i + 2\overrightarrow j – \overrightarrow k ,\overrightarrow v = – \overrightarrow i – 3\overrightarrow j + \overrightarrow k ; \cr & c)\overrightarrow u = (0;1; – 2),\overrightarrow v = (3;0; – 4) \cr & d)\overrightarrow u = 4\overrightarrow i + \overrightarrow k ,\overrightarrow v = 2\overrightarrow i – \overrightarrow {j;} \cr} \)
\(\eqalign{ & a)\left[ {\overrightarrow u ,\overrightarrow v } \right] = \left( {\left| \matrix{ 2 \hfill \cr 1 \hfill \cr} \right.\left. \matrix{ – 3 \hfill \cr 2 \hfill \cr} \right|;\left| \matrix{ – 3 \hfill \cr 2 \hfill \cr} \right.\left. \matrix{ 1 \hfill \cr – 4 \hfill \cr} \right|;\left| \matrix{ 1 \hfill \cr – 4 \hfill \cr} \right.\left. \matrix{ 2 \hfill \cr 1 \hfill \cr} \right|} \right) \cr&= (7;10;9). \cr & b)\overrightarrow u = (3;2; – 1),\overrightarrow v = ( – 1; – 3;1) \cr & \Rightarrow \left[ {\overrightarrow u ,\overrightarrow v } \right] = \left( {\left| \matrix{ 2 \hfill \cr – 3 \hfill \cr} \right.\left. \matrix{ – 1 \hfill \cr 1 \hfill \cr} \right|;\left| \matrix{ – 1 \hfill \cr 1 \hfill \cr} \right.\left. \matrix{ 3 \hfill \cr – 1 \hfill \cr} \right|;\left| \matrix{ 3 \hfill \cr – 1 \hfill \cr} \right.\left. \matrix{ 2 \hfill \cr – 3 \hfill \cr} \right|} \right)\cr& = ( – 1; – 2; – 7). \cr & c)\left[ {\overrightarrow u ,\overrightarrow v } \right] = \left( {\left| \matrix{ 1 \hfill \cr 0 \hfill \cr} \right.\left. \matrix{ – 2 \hfill \cr – 4 \hfill \cr} \right|;\left| \matrix{ – 2 \hfill \cr – 4 \hfill \cr} \right.\left. \matrix{ 0 \hfill \cr 3 \hfill \cr} \right|;\left| \matrix{ 0 \hfill \cr 3 \hfill \cr} \right.\left. \matrix{ 1 \hfill \cr 0 \hfill \cr} \right|} \right) \cr&= ( – 4; – 6; – 3). \cr & d)\overrightarrow u = (4;0;1),\overrightarrow v = (2; – 1;0) \cr & \Rightarrow \left[ {\overrightarrow u ,\overrightarrow v } \right] = \left( {\left| \matrix{ 0 \hfill \cr – 1 \hfill \cr} \right.\left. \matrix{ 1 \hfill \cr 0 \hfill \cr} \right|;\left| \matrix{ 1 \hfill \cr 0 \hfill \cr} \right.\left. \matrix{ 4 \hfill \cr 2 \hfill \cr} \right|;\left| \matrix{ 4 \hfill \cr 2 \hfill \cr} \right.\left. \matrix{ 0 \hfill \cr – 1 \hfill \cr} \right|} \right) \cr&= (1;2; – 4). \cr} \)