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Diketahui vektor a=⎝⎛​3−1−3​⎠⎞​, dan vektor b=⎝⎛​332​⎠⎞​.  a. Hitunglah a⋅b, ∣∣​a∣∣​, dan ∣∣​b∣∣​.  b. Tentukan besar sudut antara vektor a dengan vektor b.

Pertanyaan

Diketahui vektor a with rightwards arrow on top equals open parentheses table row 3 row cell negative 1 end cell row cell negative 3 end cell end table close parentheses, dan vektor b with rightwards arrow on top equals open parentheses table row 3 row 3 row 2 end table close parentheses

a. Hitunglah a with rightwards arrow on top times b with rightwards arrow on topopen vertical bar a with rightwards arrow on top close vertical bar, dan open vertical bar b with rightwards arrow on top close vertical bar

b. Tentukan besar sudut antara vektor a with rightwards arrow on top dengan vektor b with rightwards arrow on top

D. Ajeng

Master Teacher

Mahasiswa/Alumni Universitas Bengkulu

Jawaban terverifikasi

Jawaban

jawaban yang benar untuk pertanyaan a dan b seperti tersebut diatas.

Pembahasan

Jawaban yang benar untuk pertanyaan a adalah bold a with bold rightwards arrow on top bold times bold b with bold rightwards arrow on top bold equals bold 0 bold comma bold space begin bold style vertical line a with rightwards arrow on top vertical line end style bold equals square root of bold 19 bold comma bold space begin bold style vertical line b with rightwards arrow on top vertical line end style bold equals square root of bold 22 dan pertanyaan b adalah bold 90 bold degree

Ingat !

Jika diketahui vektor a with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell row cell z subscript 1 end cell end table close parentheses, dan vektor b with rightwards arrow on top equals open parentheses table row cell x subscript 2 end cell row cell y subscript 2 end cell row cell z subscript 2 end cell end table close parentheses. Maka, 

  • a with rightwards arrow on top times b with rightwards arrow on top equals x subscript 1 x subscript 2 plus y subscript 1 y subscript 2 plus z subscript 1 z subscript 2 
  • open vertical bar a with rightwards arrow on top close vertical bar equals square root of x subscript 1 squared plus y subscript 1 squared plus z subscript 1 squared end root 
  • table attributes columnalign right center left columnspacing 0px end attributes row cell cos theta end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell end table 

a. Hitunglah a with rightwards arrow on top times b with rightwards arrow on topopen vertical bar a with rightwards arrow on top close vertical bar, dan open vertical bar b with rightwards arrow on top close vertical bar

  • Menghitung nilai a with rightwards arrow on top times b with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell left parenthesis 3 times 3 right parenthesis plus left parenthesis negative 1 times 3 right parenthesis plus left parenthesis negative 3 times 2 right parenthesis end cell row blank equals cell 9 plus left parenthesis negative 3 right parenthesis plus left parenthesis negative 6 right parenthesis end cell row blank equals 0 end table 

  • Menghitung nilai open vertical bar a with rightwards arrow on top close vertical bar

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top close vertical bar end cell equals cell square root of 3 squared plus open parentheses negative 1 close parentheses squared plus left parenthesis negative 3 right parenthesis squared end root end cell row blank equals cell square root of 9 plus 1 plus 9 end root end cell row blank equals cell square root of 19 end cell end table 

  • Menghitung nilai open vertical bar b with rightwards arrow on top close vertical bar 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of 3 squared plus 3 squared plus 2 squared end root end cell row blank equals cell square root of 9 plus 9 plus 4 end root end cell row blank equals cell square root of 22 end cell end table 

b. Tentukan besar sudut antara vektor a with rightwards arrow on top dengan vektor b with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell cos theta end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row cell cos theta end cell equals cell fraction numerator 0 over denominator square root of 19 square root of 22 end fraction end cell row cell cos theta end cell equals 0 row theta equals cell a r c space cos space 0 end cell row theta equals cell 90 degree end cell end table 

Dengan demikian, jawaban yang benar untuk pertanyaan a dan b seperti tersebut diatas.

43

4.3 (3 rating)

Pertanyaan serupa

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Jawaban terverifikasi

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