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Pertanyaan

Diberikan u = 2 a − 3 b dan v = a + 4 b . Nyatakan dalam a → dan b → setiap operasi vektor berikut: u − 3 v − 2 ( 2 u − v )

Diberikan  dan . Nyatakan dalam dan  setiap operasi vektor berikut:

   

  1. ... 

  2. ... 

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A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

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 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u with rightwards arrow on top minus 3 v with rightwards arrow on top minus 2 left parenthesis 2 u with rightwards arrow on top minus v with rightwards arrow on top right parenthesis end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top end cell end table end style.

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Pembahasan

dan . Maka adalah: Jadi, .

begin mathsize 14px style u with rightwards arrow on top equals 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top end style dan begin mathsize 14px style v with rightwards arrow on top equals a with rightwards arrow on top plus 4 b with rightwards arrow on top end style. Maka begin mathsize 14px style u with rightwards arrow on top minus 3 v with rightwards arrow on top minus 2 open parentheses 2 u with rightwards arrow on top minus v with rightwards arrow on top close parentheses end style  adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u with rightwards arrow on top minus 3 v with rightwards arrow on top minus 2 left parenthesis 2 u with rightwards arrow on top minus v with rightwards arrow on top right parenthesis end cell row blank equals cell 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top minus 3 open parentheses a with rightwards arrow on top plus 4 b with rightwards arrow on top close parentheses minus 2 open parentheses 2 open parentheses 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top close parentheses minus open parentheses a with rightwards arrow on top plus 4 b with rightwards arrow on top close parentheses close parentheses end cell row blank equals cell 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top minus 3 a with rightwards arrow on top minus 12 b with rightwards arrow on top minus 2 left parenthesis 4 a with rightwards arrow on top minus 6 b with rightwards arrow on top minus a with rightwards arrow on top minus 4 b with rightwards arrow on top right parenthesis end cell row blank equals cell negative a with rightwards arrow on top minus 15 b with rightwards arrow on top minus 2 left parenthesis 3 a with rightwards arrow on top minus 10 b with rightwards arrow on top right parenthesis end cell row blank equals cell negative a with rightwards arrow on top minus 15 b with rightwards arrow on top minus 6 a with rightwards arrow on top plus 2 0 b with rightwards arrow on top end cell row blank equals cell negative 7 a with rightwards arrow on top plus 5 b with rightwards arrow on top end cell end table end style 

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u with rightwards arrow on top minus 3 v with rightwards arrow on top minus 2 left parenthesis 2 u with rightwards arrow on top minus v with rightwards arrow on top right parenthesis end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top end cell end table end style.

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Vektor a dan vektor b adalah vektor-vektor sembarang yang bukan vektor noI. Tunjukkan bahwa ( a + b ) ⋅ ( a + b ) = ∣ ∣ ​ a + b ∣ ∣ ​ 2 .

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