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Pertanyaan

Diketahui vektor-vektor, r 1 ​ ​ = 2 i + 4 j ​ − 5 k dan r 2 ​ ​ = i + 2 j ​ + 3 k . Tentukan: b. r = 2 r 1 ​ ​ − 3 r 2 ​ ​

Diketahui vektor-vektor, 

 dan .

Tentukan:

b.   

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P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell r with rightwards arrow 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 i with rightwards arrow 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell j with rightwards arrow 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 19 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell k with rightwards arrow on top end cell end table end style.

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Pembahasan

Berdasarkan informasi yang diberikan pada soal, maka dapat ditentukan pengurangan dua vektor tersebut sebagai berikut. Dengan demikian, diperoleh .

Berdasarkan informasi yang diberikan pada soal, maka dapat ditentukan pengurangan dua vektor tersebut sebagai berikut.

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 2 stack r subscript 1 with rightwards arrow on top minus 3 stack r subscript 2 with rightwards arrow on top end cell row blank equals cell 2 left parenthesis 2 i with rightwards arrow on top plus 4 j with rightwards arrow on top minus 5 k with rightwards arrow on top right parenthesis minus 3 left parenthesis i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 3 k with rightwards arrow on top right parenthesis end cell row blank equals cell left parenthesis 4 i with rightwards arrow on top plus 8 j with rightwards arrow on top minus 10 k with rightwards arrow on top right parenthesis minus left parenthesis 3 i with rightwards arrow on top plus 6 j with rightwards arrow on top plus 9 k with rightwards arrow on top right parenthesis end cell row blank equals cell left parenthesis 4 minus 3 right parenthesis i with rightwards arrow on top plus left parenthesis 8 minus 6 right parenthesis j with rightwards arrow on top plus left parenthesis negative 10 minus 9 right parenthesis k with rightwards arrow on top end cell row blank equals cell i with rightwards arrow on top plus 2 j with rightwards arrow on top minus 19 k with rightwards arrow on top end cell end table end style 

Dengan demikian, diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell r with rightwards arrow 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 i with rightwards arrow 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell j with rightwards arrow 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 19 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell k with rightwards arrow on top end cell end table end style.

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Nadiva nurhaliza Sunaryo

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