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Pertanyaan

Diberikan P A = 3 a − b , PB = 2 n a + 3 b , dan PC = 5 a + 6 b . a. Carilah vektor A B dan BC dalam a , b .

Diberikan , , dan . 

a. Carilah vektor  dan  dalam , .

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

vektor dan dalam , adalah dan

vektor A B dan B C dalam a with rightwards arrow on top, b with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack A B 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 left parenthesis 2 n minus 3 right parenthesis a with rightwards arrow on top plus 4 b with rightwards arrow on top end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack B C 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 open parentheses 5 minus 2 n close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top end cell end table 

Pembahasan

Diketahui , , dan . Maka: Jadi, vektor dan dalam , adalah dan

Diketahui stack P A with rightwards arrow on top equals 3 a with rightwards arrow on top minus b with rightwards arrow on top, stack P B with rightwards arrow on top equals 2 n a with rightwards arrow on top plus 3 b with rightwards arrow on top, dan stack P C with rightwards arrow on top equals 5 a with rightwards arrow on top plus 6 b with rightwards arrow on top. Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell stack P B with rightwards arrow on top minus stack P A with rightwards arrow on top end cell row blank equals cell open parentheses 2 n a with rightwards arrow on top plus 3 b with rightwards arrow on top close parentheses minus open parentheses 3 a with rightwards arrow on top minus b with rightwards arrow on top close parentheses end cell row blank equals cell 2 n a with rightwards arrow on top plus 3 b with rightwards arrow on top minus 3 a with rightwards arrow on top plus b with rightwards arrow on top end cell row blank equals cell left parenthesis 2 n minus 3 right parenthesis a with rightwards arrow on top plus 4 b with rightwards arrow on top end cell row blank blank blank row cell stack B C with rightwards arrow on top end cell equals cell stack P C with rightwards arrow on top minus stack P B with rightwards arrow on top end cell row blank equals cell open parentheses 5 a with rightwards arrow on top plus 6 b with rightwards arrow on top close parentheses minus open parentheses 2 n a with rightwards arrow on top plus 3 b with rightwards arrow on top close parentheses end cell row blank equals cell 5 a with rightwards arrow on top plus 6 b with rightwards arrow on top minus 2 n a with rightwards arrow on top minus 3 b with rightwards arrow on top end cell row blank equals cell open parentheses 5 minus 2 n close parentheses a with rightwards arrow on top plus 3 b with rightwards arrow on top end cell end table 

Jadi, vektor A B dan B C dalam a with rightwards arrow on top, b with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack A B 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 left parenthesis 2 n minus 3 right parenthesis a with rightwards arrow on top plus 4 b with rightwards arrow on top end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack B C 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 open parentheses 5 minus 2 n close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top end cell end table 

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