Três vetores são dados por a →   =   3,0 i ^   +   3,0 j ^ - 2,0 k ^ , b → = - 1,0 i ^   - 4,0 j ^   + 2,0 k ^ e c → =   2,0 i ^   + 2,0 j ^ +   1,0 k ^   . Determine (a) a → ⋅   ( b → ×   c → ) , (b) a → ⋅ ( b →   + c → ) e c a → ×   ( b →   + c → )

Passo 1

Então galera , nós temos que :

b → × c → =   - 8,0 i ^   +   5,0 j ^ + 6,0 k ^

Dessa forma :

a → ⋅   ( b → ×   c → ) = 3,0 - 8,0 +   3,0 5,0 +   - 2,0 6,0 =   - 21,0

Passo 2

Sabendo que :

b → + c →   = 1,0 i ^ - 2,0 j ^ + 3,0 k ^

Podemos obter :

a → ⋅   b → +   c → = 3,0 1,0 +   3,0 - 2,0 +   - 2,0 3,0 =   - 9,0

Passo 3

Ao substituirmos os valores já conhecidos , podemos obter que :

a → ×   b → +   c →   = 3,0 3,0 - - 2,0 - 2,0 i ^ + - 2,0 1,0 - 3,0 3,0 j ^ + 3,0 - 2,0 - 3,0 1,0 k ^   = 5 i ^   - 11 j ^ - 9 k ^

De boa , galera ??? Então partiu fazer mais exercícios!!!!!!

Resposta

Ei, a resposta está no passo a passo :)

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