Roboguru

Diketahui vektor: (i).  (ii).  (iii).  Diantara ketiga vektor tersebut yang merupakan vektor satuan adalah …

Pertanyaan

Diketahui vektor:

(i). u with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses

(ii). v with rightwards arrow on top equals open parentheses table row cell 2 over 5 square root of 5 end cell row cell negative 1 fifth square root of 5 end cell end table close parentheses

(iii). w with rightwards arrow on top equals open parentheses table row cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell fraction numerator negative square root of 3 over denominator 2 end fraction end cell end table close parentheses

Diantara ketiga vektor tersebut yang merupakan vektor satuan adalah …

Pembahasan Soal:

Vektor satuan adalah suatu vektor yang ternormalisasi, yang berarti panjangnya bernilai 1. Sehingga:

(i). table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row cell open vertical bar u with rightwards arrow on top close vertical bar end cell equals cell square root of left parenthesis negative 1 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared end root end cell row blank equals cell square root of 2 end cell end table

(Bukan vektor satuan)

(ii). table attributes columnalign right center left columnspacing 0px end attributes row cell v with rightwards arrow on top end cell equals cell open parentheses table row cell 2 over 5 square root of 5 end cell row cell negative 1 fifth square root of 5 end cell end table close parentheses end cell row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses 2 over 5 square root of 5 close parentheses squared plus open parentheses negative 1 fifth square root of 5 close parentheses squared end root end cell row blank equals cell square root of 4 over 5 plus 1 fifth end root end cell row blank equals cell square root of 5 over 5 end root end cell row blank equals cell square root of 1 end cell row blank equals 1 end table

(vektor satuan)

(iii). table attributes columnalign right center left columnspacing 0px end attributes row cell w with rightwards arrow on top end cell equals cell open parentheses table row cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell fraction numerator negative square root of 3 over denominator 2 end fraction end cell end table close parentheses end cell row cell open vertical bar w with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared plus open parentheses negative fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared end root end cell row blank equals cell square root of 3 over 4 plus 3 over 4 end root end cell row blank equals cell square root of 6 over 4 end root end cell row blank equals cell 1 half square root of 6 end cell end table

(bukan vektor satuan)

Jadi, diantara ketiga vektor tersebut yang merupakan vektor satuan adalah (ii)

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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