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Câu hỏi: Tính \(\left[ {\overrightarrow u ,\overrightarrow v } \right]\), \(\overrightarrow {\rm{w}} \) biết
\(\eqalign{ & a)\overrightarrow u = (0; 3; 2);\overrightarrow v = \left({ - 4; 1; 3} \right);\overrightarrow {\rm{w}} = \left({1; - 2; 2} \right); \cr & b)\overrightarrow u = 4\overrightarrow i + \overrightarrow j - 3\overrightarrow k ;\overrightarrow v = \overrightarrow j + 5\overrightarrow k ;\cr&\overrightarrow {\rm{w}} = 2\overrightarrow i - 3\overrightarrow j + \overrightarrow k ; \cr & c)\overrightarrow u = \overrightarrow i + \overrightarrow j ;\overrightarrow v = \overrightarrow i + \overrightarrow j + \overrightarrow k ;\overrightarrow {\rm{w}} = \overrightarrow i . \cr} \)
\(\eqalign{ & a)\overrightarrow u = (0; 3; 2);\overrightarrow v = \left({ - 4; 1; 3} \right);\overrightarrow {\rm{w}} = \left({1; - 2; 2} \right); \cr & b)\overrightarrow u = 4\overrightarrow i + \overrightarrow j - 3\overrightarrow k ;\overrightarrow v = \overrightarrow j + 5\overrightarrow k ;\cr&\overrightarrow {\rm{w}} = 2\overrightarrow i - 3\overrightarrow j + \overrightarrow k ; \cr & c)\overrightarrow u = \overrightarrow i + \overrightarrow j ;\overrightarrow v = \overrightarrow i + \overrightarrow j + \overrightarrow k ;\overrightarrow {\rm{w}} = \overrightarrow i . \cr} \)
Lời giải chi tiết
\(\eqalign{ & a)\left[ {\overrightarrow u ,\overrightarrow v } \right] = \left({\left| \matrix{ 3 \hfill \cr 1 \hfill \cr} \right.\left. \matrix{ 2 \hfill \cr - 3 \hfill \cr} \right|;\left| \matrix{ 2 \hfill \cr - 3 \hfill \cr} \right.\left. \matrix{ 0 \hfill \cr - 4 \hfill \cr} \right|;\left| \matrix{ 0 \hfill \cr - 4 \hfill \cr} \right.\left. \matrix{ 3 \hfill \cr 1 \hfill \cr} \right|} \right) \cr&= (- 11; - 8; 12). \cr & \Rightarrow \left[ {\overrightarrow u ,\overrightarrow v } \right].\overrightarrow {\rm{w}} = (- 11). 1 + (- 8)(- 2) + 12.2 \cr& = 29. \cr & b)\left[ {\overrightarrow u ,\overrightarrow v } \right].\overrightarrow {\rm{w}} = 80. \cr & c)\left[ {\overrightarrow u ,\overrightarrow v } \right].\overrightarrow {\rm{w}} = 1. \cr} \)
\(\eqalign{ & a)\left[ {\overrightarrow u ,\overrightarrow v } \right] = \left({\left| \matrix{ 3 \hfill \cr 1 \hfill \cr} \right.\left. \matrix{ 2 \hfill \cr - 3 \hfill \cr} \right|;\left| \matrix{ 2 \hfill \cr - 3 \hfill \cr} \right.\left. \matrix{ 0 \hfill \cr - 4 \hfill \cr} \right|;\left| \matrix{ 0 \hfill \cr - 4 \hfill \cr} \right.\left. \matrix{ 3 \hfill \cr 1 \hfill \cr} \right|} \right) \cr&= (- 11; - 8; 12). \cr & \Rightarrow \left[ {\overrightarrow u ,\overrightarrow v } \right].\overrightarrow {\rm{w}} = (- 11). 1 + (- 8)(- 2) + 12.2 \cr& = 29. \cr & b)\left[ {\overrightarrow u ,\overrightarrow v } \right].\overrightarrow {\rm{w}} = 80. \cr & c)\left[ {\overrightarrow u ,\overrightarrow v } \right].\overrightarrow {\rm{w}} = 1. \cr} \)