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Desarrollo punto 1 Wilmer Pupo.docx - DESARROLLO DE LA...

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DESARROLLO DE LA ACTIVIDAD 1. Se tienen los vectores u = 2 i + 4 j y v =− i 2 j Halle: a) La magnitud y la dirección de cada vector respecto al eje x y represéntelo en una gráfica. u = 2 i + 4 j u =( 2,4 ) Hallamos magnitud: | u | =( 2,4 ) | u | = ( 2 ) 2 +( 4 ) 2 | u | = 4 + 16 | u | = 20 | u | = 4,4721 Hallamos la dirección: tan ( α )= 4 2 α = tan 1 ( 4 2 ) α = tan 1 ( 2 ) α = 63,43 α = 63,43 °
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v =− i 2 j v =(− 1, 2 ) | v | =(− 1, 2 ) | v | = (− 1 ) 2 +(− 2 ) 2 | v | = 1 + 4 | v | = 5 | v | = 2,2360 Hallamos la dirección:
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tan ( α )= 2 1 α = tan 1 ( 2 ) α = 63,43 α = 63,43 ° Por tener sentido de las manecillas del reloj y estar en el tercer cuadrante, se le suma el valor de π que son 180º, de esta forma obtenemos el ángulo total. α = 180 ° + 63,43 ° α = 243,43 °
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b) El vector suma de u + v y el vector resta u v u + v = ( u 1 + v 1 ,u 2 + v 2 ) u + v = ( 2 + ( 1 ) , 4 +(− 2 ) ) u + v = ( 5 1,4 2 ) u + v = ( 4,2 ) u v = ( u 1 v 1 ,u 2 v 2 ) u v = ( 2 (
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