Answered

IDNLearn.com: Where your questions meet expert advice and community insights. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

5. Dados los vectores [tex]\vec{A}=(7,3)[/tex], [tex]\vec{B}=(9,10)[/tex], [tex]\vec{C}=(-4,3)[/tex], encuentre:

a) [tex]\vec{A} + \vec{B} = [/tex]

b) [tex]\vec{A} + \vec{C} = [/tex]

c) [tex]\vec{A} - \vec{B} = [/tex]

d) [tex]\vec{B} - \vec{C} = [/tex]

Sagot :

GinnyAnsweridn
Claro, vamos a encontrar las operaciones vectoriales dadas paso a paso.

### Parte a) [tex]\(\vec{A} + \vec{B}\)[/tex]

Dado que [tex]\(\vec{A}=(7,3)\)[/tex] y [tex]\(\vec{B}=(9,10)\)[/tex], sumamos estos dos vectores componente por componente:
[tex]\[ \vec{A} + \vec{B} = (7 + 9, 3 + 10) = (16, 13) \][/tex]

Entonces, [tex]\(\vec{A} + \vec{B} = (16, 13)\)[/tex].

### Parte b) [tex]\(\vec{A} + \vec{C}\)[/tex]

Dado que [tex]\(\vec{A}=(7,3)\)[/tex] y [tex]\(\vec{C}=(-4,3)\)[/tex], sumamos estos dos vectores componente por componente:
[tex]\[ \vec{A} + \vec{C} = (7 - 4, 3 + 3) = (3, 6) \][/tex]

Entonces, [tex]\(\vec{A} + \vec{C} = (3, 6)\)[/tex].

### Parte c) [tex]\(\vec{A} - \vec{B}\)[/tex]

Dado que [tex]\(\vec{A}=(7,3)\)[/tex] y [tex]\(\vec{B}=(9,10)\)[/tex], restamos estos dos vectores componente por componente:
[tex]\[ \vec{A} - \vec{B} = (7 - 9, 3 - 10) = (-2, -7) \][/tex]

Entonces, [tex]\(\vec{A} - \vec{B} = (-2, -7)\)[/tex].

### Parte d) [tex]\(\vec{B} - \vec{C}\)[/tex]

Dado que [tex]\(\vec{B}=(9,10)\)[/tex] y [tex]\(\vec{C}=(-4,3)\)[/tex], restamos estos dos vectores componente por componente:
[tex]\[ \vec{B} - \vec{C} = (9 - (-4), 10 - 3) = (9 + 4, 10 - 3) = (13, 7) \][/tex]

Entonces, [tex]\(\vec{B} - \vec{C} = (13, 7)\)[/tex].

Resumiendo las respuestas:
a) [tex]\(\vec{A} + \vec{B} = (16, 13)\)[/tex]

b) [tex]\(\vec{A} + \vec{C} = (3, 6)\)[/tex]

c) [tex]\(\vec{A} - \vec{B} = (-2, -7)\)[/tex]

d) [tex]\(\vec{B} - \vec{C} = (13, 7)\)[/tex]
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.