Question

Dados los vectores u=(3,5,7),v=(1,2,4),y w=(9,-2,3), y los escalares a=2 y b=-7 verifique si:

i) (u+v)+w=u+(v+w)=(u+w)+v
ii) Calcular: au-(v+bw)

Answer 1

Dados los vectores u, v, w y los escalares a y b.

i) (13,5,14) = (13,5,14) = (13,5,14)

ii) au-(v+bw) = (68,-6,31)

Explicación paso a paso:

Datos;

u = (3,5,7)

v = (1,2,4)

w = (9,-2,3)

a = 2  

b = -7

Aplicar suma de vectores;

i) (u+v)+w=u+(v+w)=(u+w)+v

(u+v)+w = [(3,5,7)+(1,2,4)] +(9,-2,3)

(u+v)+w = (3+1, 5+2, 7+4) + (9,-2,3)

(u+v)+w = (4,7,11) + (9,-2,3)

(u+v)+w = (13, 5, 14)

u+(v+w) =  (3,5,7) + [(1,2,4)] +(9,-2,3)]

u+(v+w) =  (3,5,7) + (10,0,7)

u+(v+w) = (13,5,14)

(u+w)+v  = [(3,5,7) + (9,-2,3)] + (1,2,4)

(u+w)+v  = (12,3,10) + (1,2,4)

(u+w)+v  = (13,5,14)

ii) Calcular: au-(v+bw)

Aplicar suma, resta y producto de un escalar por un vector;

au-(v+bw) = 2(3,5,7) - [(1,2,4)+(-7)(9,-2,3)]

au-(v+bw) = (6,10,14) - [(1,2,4)+(-63,14,-21)]

au-(v+bw) = (6,10,14) - (-62,16,-17)

au-(v+bw) = (68,-6,31)