Tentukan besar sudut yang dibentuk oleh dua vektor berikut:       c.  Vektor u=i−4j​+2k dan vektor v=3i+5j​−k.

Pertanyaan

Tentukan besar sudut yang dibentuk oleh dua vektor berikut:

      c.  Vektor u with rightwards arrow on top equals i with hat on top minus 4 j with hat on top plus 2 k with hat on top dan vektor v with rightwards arrow on top equals 3 i with hat on top plus 5 j with hat on top minus k with hat on top.

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Master Teacher

Jawaban terverifikasi

Jawaban

 besar sudut yang dibentuk oleh vektor u with rightwards arrow on top equals i with hat on top minus 4 j with hat on top plus 2 k with hat on top dan vektor v with rightwards arrow on top equals 3 i with hat on top plus 5 j with hat on top minus k with hat on top adalah 134 comma 5 degree.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell bold 134 bold comma bold 5 bold degree end cell end table.

Ingat!

  • Rumus untuk menentukan nilai cosinus antara vektor a with rightwards arrow on top dan vektor b with rightwards arrow on top adalah sebagai berikut:

cos space theta equals fraction numerator a with rightwards arrow on top space. space 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 

  • Rumus untuk menentukan panjang vektor r with rightwards arrow on top equals x i with hat on top plus y j with hat on top plus z k with hat on top adalah sebagai  berikut:

open vertical bar r with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root 

  • Rumus untuk menentukan hasil kali a with rightwards arrow on top space. space b with rightwards arrow on top jika diketahui vektor a with rightwards arrow on top equals x subscript 1 i with hat on top plus y subscript 1 j with hat on top plus z subscript 1 k with hat on top dan vektor b with rightwards arrow on top equals x subscript 2 i with hat on top plus y subscript 2 j with hat on top plus z subscript 2 k with hat on top adalah sebagai berikut:

a with rightwards arrow on top. space 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  

Diketahui:

Vektor u with rightwards arrow on top equals i with hat on top minus 4 j with hat on top plus 2 k with hat on top 

Vektor v with rightwards arrow on top equals 3 i with hat on top plus 5 j with hat on top minus k with hat on top

Ditanya: besar sudut  yang dibentuk dua vektor.

Jawab:

Dengan menggunakan rumus-rumus di atas, maka besar sudut yang dibentuk oleh vektor u with rightwards arrow on top dan vektor v with rightwards arrow on top adalah sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator u with rightwards arrow on top space. space v with rightwards arrow on top over denominator open vertical bar u with rightwards arrow on top close vertical bar open vertical bar v with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 1 cross times 3 plus open parentheses negative 4 close parentheses cross times 5 plus 2 cross times open parentheses negative 1 close parentheses over denominator open parentheses square root of 1 squared plus open parentheses negative 4 close parentheses squared plus 2 squared end root close parentheses open parentheses square root of 3 squared plus 5 squared plus open parentheses negative 1 close parentheses squared end root close parentheses end fraction end cell row blank equals cell fraction numerator 3 minus 20 minus 2 over denominator open parentheses square root of 1 plus 16 plus 4 end root close parentheses open parentheses square root of 9 plus 25 plus 1 end root close parentheses end fraction end cell row blank equals cell fraction numerator negative 19 over denominator open parentheses square root of 21 close parentheses open parentheses square root of 35 close parentheses end fraction end cell row blank equals cell fraction numerator negative 19 over denominator square root of 735 end fraction end cell row blank left right double arrow cell theta equals cos to the power of negative 1 end exponent open parentheses fraction numerator negative 19 over denominator square root of 735 end fraction close parentheses equals 134 comma 5 degree end cell end table 

Dengan demikian, besar sudut yang dibentuk oleh vektor u with rightwards arrow on top equals i with hat on top minus 4 j with hat on top plus 2 k with hat on top dan vektor v with rightwards arrow on top equals 3 i with hat on top plus 5 j with hat on top minus k with hat on top adalah 134 comma 5 degree.

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Pertanyaan serupa

Tentukan besar sudut yang dibentuk oleh dua vektor berikut:       b.  Vektor u=5i+j​−3k dan vektor v=2i+3j​+4k.

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Jawaban terverifikasi

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