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Ejercicios resueltos de Vectores y Operaciones con vectores

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Ejercicios Matem√°ticas Vectores Operaciones con vectores

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Ejercicios Resueltos

Operaciones con vectores

Listado

ej_4a5dbb468d24f

Dados los vectores:

%$ \[ \vec{a} = (2,-1,4) \] $%, %$ \[ \vec{b} = (-1,0,3) \] $%, %$ \[ \vec{c} = \left( -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right) \] $%, %$ \[ \vec{d} = \left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right) \] $%, %$ \[ \vec{e} = \left( -\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}} \right) \] $%

Realizar, cuando sea posible, las siguientes operaciones:

1. %$ \[ 3\vec{a} - 5 \vec{b} \] $%
2. %$ \[ (\vec{c} - \vec{d})\cdot \vec{e} \] $%
3. %$ \[ \vec{c} \cdot \vec{d} + \vec{e} \cdot \vec{c} \] $%
4. %$ \[ \vec{a} \cdot \vec{b} + \vec{e} \] $%
5. %$ \[ \vec{c} + 3\vec{d} - \vec{e} \] $%
6. %$ \[ \vec{a} \cdot \vec{e} \] $%

ej_4b9a642350058

Un estudiante se mueve 8 Km al norte y 6 Km al este.

¬Ņcual es la suma vectorial de estos dos trayectos? con grafica

ej_4a5dba932625c

Determinar si son linealmente dependientes o independientes los siguientes conjuntos de vectores:

%$ \[ \left{ (3,1), (6,2) \right} \] $%

ej_4a5dbafe2dc6d

Calcular la norma de los siguientes vectores

%$ \[ \vec{a} = (2,-1,4) \] $%

%$ \[ \vec{b} = (-1,0,3) \] $%

%$ \[ \vec{c} = \left( -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right) \] $%

%$ \[ \vec{d} = \left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right) \] $%

%$ \[ \vec{e} = \left( -\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}} \right) \] $%

ej_4bf95544afe76

a=(-1,-2,3), b=(1,2,4), c=(1,0,3)

siendo a,b y c vertices de un triangulo, hallar:

los angulos interiores del triangulo

las medidas de sus lados

las tres alturas y las tres medianas

 

ej_4c47284d06592

calcular el vector resultante de 100v170¬įy100v50¬į identifique sus componente restangulares,modulo y argumento

ej_4c8fff5f4fdd7

Un avion que sale del aeropurto y vuela 300km al este luego 350km a 30grados al noroeste y luego 150km al norte para finalmente llegar al punto B.

ej_4c9008ed5f1fb

  • determinar¬† la magnitud¬† de la fuerza¬† resultante¬† f1=600 n f2= 800 n y su direccion ,medida en sentido contrario¬†al giro de las manecillas del reloj¬† angulo 60¬į, angulo 45¬į

ej_4d6b2210ec559

2. Suma y resta los siguientes vectores dados en coordenadas cartesianas:

 a. (-1, 6) y (5, 8)

 b. (0, 5),(-1, -7) y (2.5, -7.5)

 c. (0, -3.4, 0),( -3.5, -10, 6.8),(1,1,1) y (-7.2, 8, 8)

ej_4d0cccb553ec9

Dos vectores tienen una resultante máxima que mide 14 m, y una resultante mínima que mide 2m.

¬ŅCu√°l es el m√≥dulo de la resultante de dicho vector cuando forma un √°ngulo recto?

ej_4af3a92dde32f

en el triangulo rectangulo ABC : AC=4m, BC=2m. si M es punto medio del catetoBC, calcula AC + AM

ej_4bdca4be34662

la suma  1569+13456
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