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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 →

Diberikan  dan . Nyatakan dalam dan  setiap operasi vektor berikut:

  

  1. ... 

  2. ... 

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A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell v with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank 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 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 9 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 : 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 size 14px u with size 14px rightwards arrow on top size 14px plus size 14px 3 size 14px v with size 14px rightwards arrow on top:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top plus 3 v with rightwards arrow on top end cell equals cell 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus 3 open parentheses a with rightwards arrow on top plus 4 b with rightwards arrow on top close parentheses end cell row blank equals cell 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus 3 a with rightwards arrow on top plus 12 b with rightwards arrow on top end cell row blank equals cell 5 a with rightwards arrow on top plus 9 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 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell v with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank 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 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 9 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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