Dados os vetores u = ( 2,3,1) e v = ( 1,4, 5) . Assinale a alternativa que expressa o resultado do produto (2u ‑3v )·(u +2v ).
a) 300
b) -300
c) 150
d) 208
e) -205
Soluções para a tarefa
Respondido por
20
Boa tarde Roger!
Solução!
Vamos fazer a multiplicação da expressão dos vetores U e V.
![(2u-3v)\times(u+2v)\\\\\
2(u^{2})+4uv-3vu-6(v^{2})\\\\\\\
2(u^{2})+uv-6(v^{2})\\\\\\\
Substituindo ~~os~~ vetores!](https://tex.z-dn.net/?f=%282u-3v%29%5Ctimes%28u%2B2v%29%5C%5C%5C%5C%5C%0A2%28u%5E%7B2%7D%29%2B4uv-3vu-6%28v%5E%7B2%7D%29%5C%5C%5C%5C%5C%5C%5C%0A2%28u%5E%7B2%7D%29%2Buv-6%28v%5E%7B2%7D%29%5C%5C%5C%5C%5C%5C%5C%0ASubstituindo+%7E%7Eos%7E%7E+vetores%21%0A "(2u-3v)\times(u+2v)\\\\\
2(u^{2})+4uv-3vu-6(v^{2})\\\\\\\
2(u^{2})+uv-6(v^{2})\\\\\\\
Substituindo ~~os~~ vetores!")
![\vec{u}=(2,3,1)~~~~~~~~~~\vec{v}=(1,4,5)\\\\\\\\
2(2,3,1 )^{2}+(2,3,1).(1,4,5)-6(1,4,5)^{2}\\\\\\\
2(4,9,1 )+(2,12,5)-6(1,16,25)\\\\\\\
(8,18,2 )+(2,12,5)+(-6,-96,-150)\\\\\\\
(10-6+30-96+7-150)\\\\\\\
(4-66-143)\\\\\\
(4-209)=-205](https://tex.z-dn.net/?f=%5Cvec%7Bu%7D%3D%282%2C3%2C1%29%7E%7E%7E%7E%7E%7E%7E%7E%7E%7E%5Cvec%7Bv%7D%3D%281%2C4%2C5%29%5C%5C%5C%5C%5C%5C%5C%5C%0A+2%282%2C3%2C1+%29%5E%7B2%7D%2B%282%2C3%2C1%29.%281%2C4%2C5%29-6%281%2C4%2C5%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0A+2%284%2C9%2C1+%29%2B%282%2C12%2C5%29-6%281%2C16%2C25%29%5C%5C%5C%5C%5C%5C%5C%0A%288%2C18%2C2+%29%2B%282%2C12%2C5%29%2B%28-6%2C-96%2C-150%29%5C%5C%5C%5C%5C%5C%5C%0A%2810-6%2B30-96%2B7-150%29%5C%5C%5C%5C%5C%5C%5C%0A%284-66-143%29%5C%5C%5C%5C%5C%5C%0A%284-209%29%3D-205%0A "\vec{u}=(2,3,1)~~~~~~~~~~\vec{v}=(1,4,5)\\\\\\\\
2(2,3,1 )^{2}+(2,3,1).(1,4,5)-6(1,4,5)^{2}\\\\\\\
2(4,9,1 )+(2,12,5)-6(1,16,25)\\\\\\\
(8,18,2 )+(2,12,5)+(-6,-96,-150)\\\\\\\
(10-6+30-96+7-150)\\\\\\\
(4-66-143)\\\\\\
(4-209)=-205")
Boa tarde!
Bons estudos!
Solução!
Vamos fazer a multiplicação da expressão dos vetores U e V.
Boa tarde!
Bons estudos!
Usuário anônimo:
Qualquer dúvida é só comentar.
Não tem como... tá mt bem explicado ^^ Muito obrigado amigo !
Valeu! Obrigado!
Eu que agradeço !
Perguntas interessantes