Pertanyaan

Tentukan vektor satuan dari a = ⎝ ⎛ 2 4 − 10 ⎠ ⎞ dalam bentuk vektor basis!

Tentukan vektor satuan dari $\overline{a} = ⎝ ⎛ 24 - 10 ⎠ ⎞$ dalam bentuk vektor basis!

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R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

vektor satuan dalam bentuk basis adalah .

vektor satuan dalam bentuk basis adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight a with hat on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 square root of 30 over denominator 30 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight i with bar on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 square root of 30 over denominator 15 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight j with bar on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 30 over denominator 6 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight k with bar on top end cell end table$ .

Pembahasan

Vektor satuan dari adalah Jadi, vektor satuan dalam bentuk basis adalah .

Vektor satuan dari a with bar on top equals open parentheses table row 2 row 4 row cell negative 10 end cell end table close parentheses adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with hat on top end cell equals cell fraction numerator straight a with bar on top over denominator open vertical bar straight a with bar on top close vertical bar end fraction end cell row cell straight a with hat on top end cell equals cell fraction numerator open parentheses table row 2 row 4 row cell negative 10 end cell end table close parentheses over denominator square root of 2 squared plus 4 squared plus open parentheses negative 10 close parentheses squared end root end fraction end cell row cell straight a with hat on top end cell equals cell fraction numerator open parentheses table row 2 row 4 row cell negative 10 end cell end table close parentheses over denominator square root of 4 plus 16 plus 100 end root end fraction end cell row cell straight a with hat on top end cell equals cell fraction numerator open parentheses table row 2 row 4 row cell negative 10 end cell end table close parentheses over denominator square root of 120 end fraction end cell row cell straight a with hat on top end cell equals cell fraction numerator open parentheses table row 2 row 4 row cell negative 10 end cell end table close parentheses over denominator 2 square root of 30 end fraction cross times fraction numerator square root of 30 over denominator square root of 30 end fraction end cell row cell straight a with hat on top end cell equals cell fraction numerator square root of 30 over denominator 60 end fraction open parentheses table row 2 row 4 row cell negative 10 end cell end table close parentheses end cell row cell straight a with hat on top end cell equals cell fraction numerator 2 square root of 30 over denominator 60 end fraction straight i with bar on top plus fraction numerator 4 square root of 30 over denominator 60 end fraction straight j with bar on top minus fraction numerator 10 square root of 30 over denominator 60 end fraction straight k with bar on top end cell row cell straight a with hat on top end cell equals cell fraction numerator 1 square root of 30 over denominator 30 end fraction straight i with bar on top plus fraction numerator 1 square root of 30 over denominator 15 end fraction straight j with bar on top minus fraction numerator square root of 30 over denominator 6 end fraction straight k with bar on top end cell end table$

Jadi, vektor satuan dalam bentuk basis adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight a with hat on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 square root of 30 over denominator 30 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight i with bar on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 square root of 30 over denominator 15 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight j with bar on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 30 over denominator 6 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight k with bar on top end cell end table$ .

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