Pertanyaan

Diketahui vektor a = 3 i − 2 j , b = − i + 4 j dan r = 7 i − 8 j . Jika r = k a + m b , maka nilai dari k + m = ...

Diketahui vektor $a = 3 i - 2 j, b = - i + 4 j$ dan $r = 7 i - 8 j$ . Jika $r = k a + m b$ , maka nilai dari $k + m =$ ...

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Klaim

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Diketahui dan . Mencari nilai : Didapat , sehingga . Jadi, nilai . Dengan demikian, jawaban yang tepat adalah A.

Diketahui dan .
Mencari nilai :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top end cell equals cell k a with rightwards arrow on top plus m b with rightwards arrow on top end cell row cell open parentheses table row 7 row cell negative 8 end cell end table close parentheses end cell equals cell k open parentheses table row 3 row cell negative 2 end cell end table close parentheses plus m open parentheses table row cell negative 1 end cell row 4 end table close parentheses end cell row cell open parentheses table row 7 row cell negative 8 end cell end table close parentheses end cell equals cell open parentheses table row cell 3 k end cell row cell negative 2 k end cell end table close parentheses plus open parentheses table row cell negative m end cell row cell 4 m end cell end table close parentheses end cell row cell open parentheses table row 7 row cell negative 8 end cell end table close parentheses end cell equals cell open parentheses table row cell 3 k minus m end cell row cell negative 2 k plus 4 m end cell end table close parentheses end cell row 7 equals cell 3 k minus m comma space minus 8 equals negative 2 k plus 4 m end cell row blank blank blank row 7 equals cell 3 k minus m end cell row cell 3 k end cell equals cell 7 plus m end cell row k equals cell fraction numerator 7 plus m over denominator 3 end fraction end cell row cell Substitusi thin space k end cell equals cell fraction numerator 7 plus m over denominator 3 end fraction end cell row cell negative 8 end cell equals cell negative 2 k plus 4 m end cell row cell negative 8 end cell equals cell negative 2 times fraction numerator 7 plus m over denominator 3 end fraction plus 4 m end cell row cell negative 8 end cell equals cell fraction numerator negative 14 plus 10 m over denominator 3 end fraction end cell row cell fraction numerator negative 14 plus 10 m over denominator 3 end fraction end cell equals cell negative 8 end cell row cell negative 14 plus 10 m end cell equals cell negative 24 end cell row cell 10 m end cell equals cell negative 10 end cell row m equals cell negative 1 end cell row blank blank blank row cell Substitusi space m end cell equals cell negative 1 end cell row k equals cell fraction numerator 7 plus m over denominator 3 end fraction end cell row k equals cell fraction numerator 7 minus 1 over denominator 3 end fraction end cell row k equals 2 end table end style$

Didapat , sehingga .

Jadi, nilai .

Dengan demikian, jawaban yang tepat adalah A.