EJERCICIO 1

θa = 60°

θb = 180 – 70 = 110°

ax =  20 cos 60= 10

bx = 30 cos 110= -10.26

ay = 20 sen 60 = 17.32

by = 30 sen 110  = 28.19

c = <10  – 10.26, 17.32 + 28.19>

c = 26, 45.51

EJERCICIO 2

θa = 90 – 10 =80°

θb = 35°

θc = 180 – 65 = 115°

ax = 30 cos 80= 5.21

bx = 40 cos 35 = 32.77

cx = 50 cos 115 = -21.13

ay = 30 sen  80 =  29.54

by = 40 sen 35 = 22.94

cy = 50 sen 115 = 45.32

c = <5.21 + 32.77  -21.13 , 29.54 + 22.94 +45.32>

c = 16.85, 97.8

EJERCICIO 3

Primero encontramos el ángulo positivo

θa = 165°

θb = 310°

θc = 70°

encontramos “x”

ax = 7 cos 165 = -6.76

bx = 10 cos 310 =6.43

cx = 12 cos 70 = 4.10

encontramos “y”

ay = 7 sen 165 = 1.81

by = 10 sen 310 = -7.67

cy = 12 sen 70 = 11.27

Sumamos vector resultante z

z= 3.77,  5.41

EJERCICIO 4

θa = 30°

θA = 90 + 90 + 15 =165°

encontramos “x”

ax = 25 cos 30 = 21.65

bx = 45 cos 165 =-43.47

encontramos “y”

ay = 25 sen 30 = 12.5

by = 45 sen 165 = 11.65

c= -21.82, 24.15

EJERCICIO 5

Tenemos los siguientes vectores:

vector opuesto de b:

a = 15 N

-b = 35 N

Medimos el ángulo

θa = 180-50 = 130°

θb = 180-25 = 155°

Sacamos “x”

ax = 15 cos 130° = -9.64

bx =  35 cos 155° = -31.72

Sacamos “y”

ay =  15 sen 130° = 11.49

by =  35 sen 155° = 14.79

Sumamos

a + (-b) = -41.36, 26.28