Bài 1 trang 80 SGK Hình học 12 Nâng cao

a) \(\overrightarrow u  = \left( {1; - 2;0} \right)\,;\,\overrightarrow v  = \left( {3;5; - 5} \right)\,;\,\overrightarrow {\rm{w}}  = \left( {2;3; - 1} \right)\)
b) \(\eqalign{
& \cos \left( {\overrightarrow v ,\overrightarrow i } \right) = {{\overrightarrow v .\overrightarrow i } \over {\left| {\overrightarrow v } \right|\left| {\overrightarrow i } \right|}} = {3 \over {\sqrt {59} }} \cr 
& \cos \left( {\overrightarrow v ,\overrightarrow j } \right) = {{\overrightarrow v .\overrightarrow j } \over {\left| {\overrightarrow v } \right|\left| {\overrightarrow j } \right|}} = {5 \over {\sqrt {59} }} \cr 
& \cos \left( {\overrightarrow v ,\overrightarrow k } \right) = {{\overrightarrow v .\overrightarrow k } \over {\left| {\overrightarrow v } \right|\left| {\overrightarrow k } \right|}} = {{ - 5} \over {\sqrt {59} }} \cr} \)c) \(\eqalign{
& \overrightarrow u .\overrightarrow v = 1.3 - 2.5 + 0\left( { - 5} \right) = - 7 \cr 
& \overrightarrow u .\overrightarrow w = 1.2 - 2.3 + 0\left( { - 1} \right) = - 4 \cr 
& \overrightarrow v .\overrightarrow w = 3.2 + 5.3 + (-5).(-1) = 26 \cr} \)