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