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Diketahui vector  dan  pada gambar berikut ini Jika dinyatakan dalam vektor satuan, maka

Pertanyaan

Diketahui vector p with rightwards arrow on top dan q with rightwards arrow on top pada gambar berikut ini

Jika dinyatakan dalam vektor satuan, maka

Pembahasan Soal:

Perhatikan p with rightwards arrow on top.

Arah p with rightwards arrow on top adalah 4 ke kanan dan 2 ke atas, artinya jika ditulis dalam bentuk vektor posisi adalah p with rightwards arrow on top equals left parenthesis 4 comma space 2 right parenthesis. Sehingga vektor satuannya adalah:

 table attributes columnalign right center left columnspacing 0px end attributes row cell vektor space satuan space p with rightwards arrow on top end cell equals cell fraction numerator left parenthesis 4 comma space 2 right parenthesis over denominator square root of 4 squared plus 2 squared end root end fraction end cell row blank equals cell fraction numerator left parenthesis 4 comma space 2 right parenthesis over denominator square root of 20 end fraction end cell row blank equals cell fraction numerator left parenthesis 4 comma space 2 right parenthesis over denominator 2 square root of 5 end fraction end cell row blank equals cell open parentheses fraction numerator 4 over denominator 2 square root of 5 end fraction comma space fraction numerator 2 over denominator 2 square root of 5 end fraction close parentheses end cell row blank equals cell open parentheses 2 over 5 square root of 5 comma space 1 fifth square root of 5 close parentheses end cell end table  

Perhatikan q with rightwards arrow on top.

Arah q with rightwards arrow on top adalah 2 ke kanan dan 3 ke atas, artinya jika ditulis dalam bentuk vektor posisi adalah q with rightwards arrow on top equals left parenthesis 2 comma space 3 right parenthesis. Sehingga vektor satuannya adalah:

 table attributes columnalign right center left columnspacing 0px end attributes row cell vektor space satuan space q with rightwards arrow on top end cell equals cell fraction numerator left parenthesis 2 comma space 3 right parenthesis over denominator square root of 2 squared plus 3 squared end root end fraction end cell row blank equals cell fraction numerator left parenthesis 2 comma space 3 right parenthesis over denominator square root of 13 end fraction end cell row blank equals cell open parentheses 2 over 13 square root of 13 comma space 3 over 13 square root of 13 close parentheses end cell end table  

Jadi, vektor satuan dari p with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 over 5 square root of 5 comma space 1 fifth square root of 5 close parentheses end cell end table dan vektor satuan dari q with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 over 13 square root of 13 comma space 3 over 13 square root of 13 close parentheses end cell end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Mei 2021

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