Magnitudes y vectores - 2 Vectores 10

Vectores 10. 10- Sabiendo que los vectores A y B son los dados en el ejercicio 4. Calcular para cada caso el vector D que cumple:

(I) A + D = B

(II) A + B + D = F = (10; 10).

a) A=(-3; 2) B=(-2; 5)  (Vectores del ejercicio 4.)

(I) A + D = B

A + D = ( -3 + xD; 2 + yD)

-3 + xD = -2 -------  > xD = -2 + 3 = 1

2 + yD = 5 --------- > yD = 5 – 2 = 3

------- > D = ( 1 ; 3)

(II) A + B + D = F = (10; 10).

A + B + D = ( -3 – 2 + xD; 2 + 5 + yD)

-3 – 2 + xD = 10 ----------  > xD = 10 + 3 +2 = 15

2 + 5 + yD = 10  ----------  > yD = 10 – 2 – 5 =  3

------- > D = ( 15 ; 3)

b) A tal que |A|=2 θ = 240° B tal que |B|=3 θ = 135°   (Vectores del ejercicio 4.)

Coordenadas cartesianas de los vectores A y B

Ax = |A| cos θ = 2 cos 240º = - 1

Ay = |A| sen θ = 2 sen 240º = - 1,73

Bx = |B| cos θ = 3 cos 135º = - 2,12

By = |B| sen θ = 3 sen 135º = 2,12

(I) A + D = B

A + D = ( -1 + xD; -1,73 + yD)

-1 + xD = -2,12  -------  > xD = -2,12 + 1 = -1,12

-1,73 + yD = 2,12 --------- > yD = 2,12 + 1,73 = 3,85

------- > D = ( -1,12 ; 3,85)

(II) A + B + D = F = (10; 10).

A + B + D = ( -1 – 2,12 + xD; -1,73 + 2,12 + yD)

-1 – 2,12 + xD = 10 ----------  > xD = 10 + 1 + 2,12 = 13,12

-1,73 + 2,12 + yD = 10  ----------  > yD = 10 + 1,73 - 2,12  =  9,61

------- > D = (13,12 ; 9,61)

 c) A = (-2; 2) B = (-5; 5) (Vectores del ejercicio 4.)

(I) A + D = B

A + D = ( -2 + xD; 2 + yD)

-2 + xD = -5 -------  > xD = -5 + 2  = -3

2 + yD = 5 --------- > yD = 5 – 2 = 3

------- > D = ( -3 ; 3)

(II) A + B + D = F = (10; 10).

A + B + D = ( -2 – 5 + xD; 2 + 5 + yD)

-2 – 5 + xD = 10 ----------  > xD = 10 + 2 + 5 = 17

2 + 5 + yD = 10  ----------  > yD = 10 – 2 – 5 =  3

------- > D = ( 17 ; 3)