La multiplicación de un número [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-949d2215af84212c9aa2dac4de43c4e2_l3.png[/img] por un vector [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-0c4b6499f3d2c8d97fe665f5cb2f3769_l3.png[/img] es otro vector:[br]Con igual dirección que el vector [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-0c4b6499f3d2c8d97fe665f5cb2f3769_l3.png[/img].[br]Con el mismo sentido que el vector [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-0c4b6499f3d2c8d97fe665f5cb2f3769_l3.png[/img] si [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-949d2215af84212c9aa2dac4de43c4e2_l3.png[/img] es positivo.[br]Con sentido contrario del vector [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-0c4b6499f3d2c8d97fe665f5cb2f3769_l3.png[/img] si [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-949d2215af84212c9aa2dac4de43c4e2_l3.png[/img] es negativo.[br]De módulo [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-977db5fd4097f0c57187b810352c0611_l3.png[/img].[br] [br][img]https://www.superprof.es/apuntes/wp-content/uploads/2019/07/multiplicacion-de-un-escalar-por-un-vector-6.gif[/img][br] [br]Las componentes del vector resultante se obtienen multiplicando el escalar, [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-949d2215af84212c9aa2dac4de43c4e2_l3.png[/img], por las componentes del vector.[br] [br]Si tenemos por ejemplo, el vector[br] [br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-ab20e947f025051b8a0670c83f362f52_l3.png[/img][br] [br]Y lo queremos multiplicar por un escalar [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-949d2215af84212c9aa2dac4de43c4e2_l3.png[/img], el resultado obtenido es:[br] [br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-4d2b28fa5897d52dec0b1497b8fcdae0_l3.png[/img][br]
[b]Asociativa:[/b][br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-bc83f4c4a1fd8ac91ef1e697385c5a03_l3.png[/img][br] [br][b]Distributiva:[/b][br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-695efe109efac25475c80ec0db9ceec0_l3.png[/img][br] [br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-8d12521221165387b0d604da28dd3e0c_l3.png[/img][br] [br][b]Elemento neutro: [/b][br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-f3e7ce94188e8e3ccddc62fada25cfc3_l3.png[/img][br]
Tenemos los siguientes vectores:[br] [br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-d2f04ef341d614913cfb1726e0517c9f_l3.png[/img][br] [br]Si multiplicamos el vector [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-0f8f5d423f74963f5cc731a63882d9db_l3.png[/img] por [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-6cf33ae61020e24e7a3698071918f7c9_l3.png[/img], obtenemos[br] [br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-481098f4d365c7e0eea9836123cb4d76_l3.png[/img][br] [br]Si multiplicamos el vector [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-abdcf19b09d556f826e121ff5ceb2e2b_l3.png[/img] por [img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-752cc75c4a343e253f9b1d7fbca40ba1_l3.png[/img], tenemos:[br] [br][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-c7dd8a36752c18448f39c4ae8d2c9e57_l3.png[/img][br] [br][b][img]https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-709dfd0ca80f4bd4ee525989ac44e96f_l3.png[/img][/b]