Trong mặt phẳng tọa độ xOy cho 3 điểm A ( 2,1 ) B ( 0,5 ) C ( 8,7) 1. tìm tọa độ các vecto AB + CA; CA + CB ; AB + AC; AB - BC 2. hãy tìm tọa độ các vecto 3AB ; 2CA; 5BC 3.tìm toạ độ các vecto 3AB + 2CA; 5BC + 3AB; 4BC - 2AB

$$\eqalign{ A\left( {2;1} \right) & ,\,\,B\left( {0;5} \right),\,\,C\left( {8;7} \right) \cr a)\,\,\overrightarrow {AB} = \left( { - 2;4} \right);\,\,\overrightarrow {CA} = \left( { - 6; - 6} \right) \cr \Rightarrow \overrightarrow {AB} + \overrightarrow {CA} = \left( { - 8; - 2} \right) \cr \overrightarrow {CA} = \left( { - 6; - 6} \right);\,\,\overrightarrow {CB} = \left( { - 8; - 2} \right) \cr \Rightarrow \overrightarrow {CA} + \overrightarrow {CB} = \left( { - 14; - 8} \right) \cr \overrightarrow {AB} = \left( { - 2;4} \right);\,\,\overrightarrow {AC} = \left( {6;6} \right) \cr \Rightarrow \overrightarrow {AB} + \overrightarrow {AC} = \left( {4;10} \right) \cr \overrightarrow {AB} = \left( { - 2;4} \right) \cr \overrightarrow {BC} = \left( {8;2} \right) \cr \Rightarrow \overrightarrow {AB} - \overrightarrow {BC} = \left( { - 10;2} \right) \cr 2)\,\,3\overrightarrow {AB} = 3\left( { - 2;4} \right) = \left( { - 6;12} \right) \cr \,\,\,\,\,\,2\overrightarrow {CA} = 2\left( { - 6; - 6} \right) = \left( { - 12; - 12} \right) \cr \,\,\,\,\,\,5\overrightarrow {BC} = 5\left( {8;2} \right) = \left( {40;10} \right) \cr 3)\,\,3\overrightarrow {AB} + 2\overrightarrow {CA} = 3\left( { - 2;4} \right) + 2\left( { - 6; - 6} \right) \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( { - 6;12} \right) + \left( { - 12; - 12} \right) = \left( { - 18;0} \right) \cr \,\,\,\,\,5\overrightarrow {BC} + 3\overrightarrow {AB} = 5\left( {8;2} \right) + 3\left( { - 2;4} \right) = \left( {34;22} \right) \cr \,\,\,\,4\overrightarrow {BC} - 2\overrightarrow {AB} = 4\left( {8;2} \right) - 2\left( { - 2;4} \right) = \left( {36;0} \right) \cr} $$