Bài 9 trang 117 Sách bài tập Hình học lớp 12 Nâng cao
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Tính
(eqalign{ & a)overrightarrow u = (1;2; - 3),overrightarrow v = ( - 4;1;2); cr & b)overrightarrow u = 3overrightarrow i + 2overrightarrow j - overrightarrow k ,overrightarrow v = - overrightarrow i - 3overrightarrow j + overrightarrow k ; cr & c)overrightarrow u = (0;1; - 2),overrightarrow v = (3;0; - 4) cr & d)overrightarrow u = 4overrightarrow i + overrightarrow k ,overrightarrow v = 2overrightarrow i - overrightarrow {j;} cr} )
Giải
(eqalign{ & a)left[ {overrightarrow u ,overrightarrow v } ight] = left( {left| matrix{ 2 hfill cr 1 hfill cr} ight.left. matrix{ - 3 hfill cr 2 hfill cr} ight|;left| matrix{ - 3 hfill cr 2 hfill cr} ight.left. matrix{ 1 hfill cr - 4 hfill cr} ight|;left| matrix{ 1 hfill cr - 4 hfill cr} ight.left. matrix{ 2 hfill cr 1 hfill cr} ight|} ight) cr&= (7;10;9). cr & b)overrightarrow u = (3;2; - 1),overrightarrow v = ( - 1; - 3;1) cr & Rightarrow left[ {overrightarrow u ,overrightarrow v } ight] = left( {left| matrix{ 2 hfill cr - 3 hfill cr} ight.left. matrix{ - 1 hfill cr 1 hfill cr} ight|;left| matrix{ - 1 hfill cr 1 hfill cr} ight.left. matrix{ 3 hfill cr - 1 hfill cr} ight|;left| matrix{ 3 hfill cr - 1 hfill cr} ight.left. matrix{ 2 hfill cr - 3 hfill cr} ight|} ight)cr& = ( - 1; - 2; - 7). cr & c)left[ {overrightarrow u ,overrightarrow v } ight] = left( {left| matrix{ 1 hfill cr 0 hfill cr} ight.left. matrix{ - 2 hfill cr - 4 hfill cr} ight|;left| matrix{ - 2 hfill cr - 4 hfill cr} ight.left. matrix{ 0 hfill cr 3 hfill cr} ight|;left| matrix{ 0 hfill cr 3 hfill cr} ight.left. matrix{ 1 hfill cr 0 hfill cr} ight|} ight) cr&= ( - 4; - 6; - 3). cr & d)overrightarrow u = (4;0;1),overrightarrow v = (2; - 1;0) cr & Rightarrow left[ {overrightarrow u ,overrightarrow v } ight] = left( {left| matrix{ 0 hfill cr - 1 hfill cr} ight.left. matrix{ 1 hfill cr 0 hfill cr} ight|;left| matrix{ 1 hfill cr 0 hfill cr} ight.left. matrix{ 4 hfill cr 2 hfill cr} ight|;left| matrix{ 4 hfill cr 2 hfill cr} ight.left. matrix{ 0 hfill cr - 1 hfill cr} ight|} ight) cr&= (1;2; - 4). cr} )
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