Question

Realiza las siguientes operaciones con los vectores dados:

Answer 1

El resultado de las operaciones con vectores:

A) (2, -1, -2, 0)

B) (34, -20, 50, 8)

C) (-78, 48, -66, -12)

D) (27, -17, 5, 2)

Explicación:

Dados;

u = (-3, 2, 1, 0)

v = (5, -3, 6, 1)

w = (3, -2, 8, 1)

A) v - w (resta de vectores)

sustituir;

= (5, -3, 6, 1)- (3, -2, 8, 1)

= (5-3, -3+2, 6-8, 1-1)

= (2, -1, -2, 0)

B) 2u + 8v

escalar por un vector;

2u = 2(-3, 2, 1, 0)

2u = (-6, 4, 2, 0)

8v = 8(5, -3, 6, 1)

8v = (40, -24, 48, 8)

Sustituir;

= (-6, 4, 2, 0) + (40, -24, 48, 8)

= (-6+40, 4-24, 2+48, 0+8)

= (34, -20, 50, 8)

C) 6(u-2v)

2v = 2(5, -3, 6, 1)

2v = (10, -6, 12, 2)

Sustituir;

= 6[(-3, 2, 1, 0)- (10, -6, 12, 2)]

= 6(-3-10, 2+6, 1-12, 0-2)

= 6(-13, 8, -11, -2)

= (-78, 48, -66, -12)

D) (4v - w)- (5u + v)

4v = 4(5, -3, 6, 1)

4v = (20, -12, 24, 4)

5u = 5(-3, 2, 1, 0)

5u = (-15, 10, 5, 0)

sustituir;

= [(20, -12, 24, 4) - (3, -2, 8, 1)] - [(-15, 10, 5, 0)+(5, -3, 6, 1)]

= (20-3, -12+2, 24-8, 4-1) - (-15+5, 10-3, 5+6, 0+1)

= (17, -10, 16, 3) - (-10, 7, 11, 1)

= (27, -17, 5, 2)