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Tentukan besar sudut yang dibentuk oleh dua vektor berikut:  Vektor u=4i+7j​+4k dan vektor v=6i+5j​+3k.

Pertanyaan

Tentukan besar sudut yang dibentuk oleh dua vektor berikut:

  1.  Vektor u with rightwards arrow on top equals 4 i with hat on top plus 7 j with hat on top plus 4 k with hat on top dan vektor v with rightwards arrow on top equals 6 i with hat on top plus 5 j with hat on top plus 3 k with hat on top.

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

 besar sudut yang dibentuk vektor u with rightwards arrow on top equals 4 i with hat on top plus 7 j with hat on top plus 4 k with hat on top dan vektor v with rightwards arrow on top equals 6 i with hat on top plus 5 j with hat on top plus 3 k with hat on top adalah 19 comma 45 degree.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah bold 19 bold comma bold 45 bold degree.

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 4 i with hat on top plus 7 j with hat on top plus 4 k with hat on top

Vektor v with rightwards arrow on top equals 6 i with hat on top plus 5 j with hat on top plus 3 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 4 cross times 6 plus 7 cross times 5 plus 4 cross times 3 over denominator open parentheses square root of 4 squared plus 7 squared plus 4 squared end root close parentheses open parentheses square root of 6 squared plus 5 squared plus 3 squared end root close parentheses end fraction end cell row blank equals cell fraction numerator 24 plus 35 plus 12 over denominator open parentheses square root of 16 plus 49 plus 16 end root close parentheses open parentheses square root of 36 plus 25 plus 9 end root close parentheses end fraction end cell row blank equals cell fraction numerator 71 over denominator open parentheses square root of 81 close parentheses open parentheses square root of 70 close parentheses end fraction end cell row blank equals cell fraction numerator 71 over denominator 9 square root of 70 end fraction end cell row theta equals cell cos to the power of negative 1 end exponent open parentheses fraction numerator 71 over denominator 9 square root of 70 end fraction close parentheses end cell row theta equals cell 19 comma 45 degree end cell end table 

Dengan demikian, besar sudut yang dibentuk vektor u with rightwards arrow on top equals 4 i with hat on top plus 7 j with hat on top plus 4 k with hat on top dan vektor v with rightwards arrow on top equals 6 i with hat on top plus 5 j with hat on top plus 3 k with hat on top adalah 19 comma 45 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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