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