Diketahui vektor, dan vektor, . Vektor, adalah resultan dari vektor, dengan vektor, ., c. Tentukanlah vektor-vektor satuan dari vektor, ,vektor, , danvektor, .

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PERTANYAAN :

Diketahui vektor u with rightwards arrow on top equals open parentheses table row 2 row 4 row cell negative 5 end cell end table close parentheses dan vektor v with rightwards arrow on top equals open parentheses table row 1 row 2 row 3 end table close parentheses. Vektor w with rightwards arrow on top adalah resultan dari vektor u with rightwards arrow on top dengan vektor v with rightwards arrow on top.

c. Tentukanlah vektor-vektor satuan dari vektor u with rightwards arrow on top, vektor v with rightwards arrow on top, dan vektor w with rightwards arrow on top.

Table of Contents

Jawaban

diperoleh vektor satuan u with rightwards arrow on top adalah e with hat on top equals open parentheses table row cell fraction numerator 2 over denominator 3 square root of 5 end fraction end cell row cell fraction numerator 4 over denominator 3 square root of 5 end fraction end cell row cell negative fraction numerator 5 over denominator 3 square root of 5 end fraction end cell end table close parentheses, vektor satuan v with rightwards arrow on top adalah e with hat on top equals open parentheses table row cell fraction numerator 1 over denominator square root of 14 end fraction end cell row cell fraction numerator 2 over denominator square root of 14 end fraction end cell row cell fraction numerator 3 over denominator square root of 14 end fraction end cell end table close parentheses, dan vektor satuan w with rightwards arrow on top adalah e with hat on top equals open parentheses table row cell 3 over 7 end cell row cell 6 over 7 end cell row cell negative 2 over 7 end cell end table close parentheses 


Pembahasan

Jawaban yang benar untuk pertanyaan tersebut, yaitu vektor satuan bold italic u with bold italic rightwards arrow on top adalah Error converting from MathML to accessible text., vektor satuan bold italic v with bold italic rightwards arrow on top adalah Error converting from MathML to accessible text., dan vektor satuan bold w with bold rightwards arrow on top adalah Error converting from MathML to accessible text. 

Misalkan diketahui vektor a with rightwards arrow on top equals open parentheses table row cell x subscript a end cell row cell y subscript a end cell row cell z subscript a end cell end table close parentheses. Panjang atau besar vektor a with rightwards arrow on top ditentukan dengan rumus:

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

Vektor satuan dari a with rightwards arrow on top, dilambangkan dengan e with hat on top, ditentukan dengan rumus:

e with hat on top equals fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction equals fraction numerator 1 over denominator square root of x subscript a squared plus y subscript a squared plus z subscript a squared end root end fraction open parentheses table row cell x subscript a end cell row cell y subscript a end cell row cell z subscript a end cell end table close parentheses

  • Vektor satuan dari vektor u with rightwards arrow on top dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar u with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of 2 squared plus 4 squared plus open parentheses negative 5 close parentheses squared end root end cell row blank equals cell square root of 4 plus 16 plus 25 end root end cell row blank equals cell square root of 45 end cell row blank equals cell 3 square root of 5 end cell end table

Diperoleh vektor satuan:

e with hat on top equals fraction numerator u with rightwards arrow on top over denominator open vertical bar u with rightwards arrow on top close vertical bar end fraction equals fraction numerator 1 over denominator 3 square root of 5 end fraction open parentheses table row 2 row 4 row cell negative 5 end cell end table close parentheses equals open parentheses table row cell fraction numerator 2 over denominator 3 square root of 5 end fraction end cell row cell fraction numerator 4 over denominator 3 square root of 5 end fraction end cell row cell negative fraction numerator 5 over denominator 3 square root of 5 end fraction end cell end table close parentheses

  • Vektor satuan dari vektor v with rightwards arrow on top dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of 1 squared plus 2 squared plus 3 squared end root end cell row blank equals cell square root of 1 plus 4 plus 9 end root end cell row blank equals cell square root of 14 end cell end table

Diperoleh vektor satuan:

e with hat on top equals fraction numerator v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar end fraction equals fraction numerator 1 over denominator square root of 14 end fraction open parentheses table row 1 row 2 row 3 end table close parentheses equals open parentheses table row cell fraction numerator 1 over denominator square root of 14 end fraction end cell row cell fraction numerator 2 over denominator square root of 14 end fraction end cell row cell fraction numerator 3 over denominator square root of 14 end fraction end cell end table close parentheses

  • Vektor w with rightwards arrow on top dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell w with rightwards arrow on top end cell equals cell u with rightwards arrow on top plus v with rightwards arrow on top equals open parentheses table row 2 row 4 row cell negative 5 end cell end table close parentheses plus open parentheses table row 1 row 2 row 3 end table close parentheses equals open parentheses table row 3 row 6 row cell negative 2 end cell end table close parentheses end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar w with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of 3 squared plus 6 squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 9 plus 36 plus 4 end root end cell row blank equals cell square root of 49 end cell row blank equals 7 end table

Diperoleh vektor satuan:

e with hat on top equals fraction numerator w with rightwards arrow on top over denominator open vertical bar w with rightwards arrow on top close vertical bar end fraction equals 1 over 7 open parentheses table row 3 row 6 row cell negative 2 end cell end table close parentheses equals open parentheses table row cell 3 over 7 end cell row cell 6 over 7 end cell row cell negative 2 over 7 end cell end table close parentheses

Dengan demikian, diperoleh vektor satuan u with rightwards arrow on top adalah e with hat on top equals open parentheses table row cell fraction numerator 2 over denominator 3 square root of 5 end fraction end cell row cell fraction numerator 4 over denominator 3 square root of 5 end fraction end cell row cell negative fraction numerator 5 over denominator 3 square root of 5 end fraction end cell end table close parentheses, vektor satuan v with rightwards arrow on top adalah e with hat on top equals open parentheses table row cell fraction numerator 1 over denominator square root of 14 end fraction end cell row cell fraction numerator 2 over denominator square root of 14 end fraction end cell row cell fraction numerator 3 over denominator square root of 14 end fraction end cell end table close parentheses, dan vektor satuan w with rightwards arrow on top adalah e with hat on top equals open parentheses table row cell 3 over 7 end cell row cell 6 over 7 end cell row cell negative 2 over 7 end cell end table close parentheses 


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