a=7i+5j−3k b=5i+2j+3k, dan c=a−b. Tentukan vektor satuan yang berlawanan dengan c adalah ....

Pertanyaan

$\style{font-size:14px}{\overrightarrow a=7\overrightarrow i+5\overrightarrow j-3\overrightarrow k}$
$\style{font-size:14px}{\overrightarrow b=5\overrightarrow i+2\overrightarrow j+3\overrightarrow k}$ , dan
$\style{font-size:14px}{\overrightarrow c=\overrightarrow a-\overrightarrow b}$ .

Tentukan vektor satuan yang berlawanan dengan $\style{font-size:14px}{\overrightarrow c}$ adalah ....

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

vektor satuan yang berlawanan dengan

adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative fraction numerator 2 over denominator square root of 19 end fraction end cell row cell negative fraction numerator 3 over denominator square root of 19 end fraction end cell row cell fraction numerator 6 over denominator square root of 19 end fraction end cell end table close parentheses end cell end table end style$

Pembahasan

Diberikan vektor . Dimisalkan vektor adalah vektor yang berlawanan arah dengan vektor .

Vektor satuan dari vektor adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with hat on top end cell equals cell fraction numerator top enclose p over denominator open vertical bar top enclose p close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 2 end cell row cell negative 3 end cell row 6 end table close parentheses over denominator square root of left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 3 right parenthesis squared plus 6 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 4 plus 9 plus 6 end root end fraction times open parentheses table row cell negative 2 end cell row cell negative 3 end cell row 6 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 19 end fraction times open parentheses table row cell negative 2 end cell row cell negative 3 end cell row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative fraction numerator 2 over denominator square root of 19 end fraction end cell row cell negative fraction numerator 3 over denominator square root of 19 end fraction end cell row cell fraction numerator 6 over denominator square root of 19 end fraction end cell end table close parentheses end cell end table end style$

Jadi, vektor satuan yang berlawanan dengan adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative fraction numerator 2 over denominator square root of 19 end fraction end cell row cell negative fraction numerator 3 over denominator square root of 19 end fraction end cell row cell fraction numerator 6 over denominator square root of 19 end fraction end cell end table close parentheses end cell end table end style$