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Diketahui vektor a=i+3j​−2k dan b=4i−2j​+4k. Tentukanlah (2a + b)⋅(a−2b).

Pertanyaan

Diketahui vektor top enclose a equals top enclose i plus 3 top enclose j minus 2 top enclose k dan top enclose b equals 4 top enclose i minus 2 top enclose j plus 4 top enclose k. Tentukanlah left parenthesis 2 top enclose a space plus space top enclose b right parenthesis times left parenthesis top enclose a minus 2 top enclose b right parenthesis.

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

hasil dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 top enclose a space plus space top enclose b right parenthesis times left parenthesis top enclose a minus 2 top enclose b right parenthesis end cell end table adalah 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 42 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose i 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 28 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose j end cell end table

Pembahasan

Ingat kembali:

Jika top enclose u equals a top enclose i plus b top enclose j plus c top enclose k space d a n space top enclose v equals d top enclose i plus e top enclose j plus f top enclose k , maka:

top enclose u times top enclose v equals a times d top enclose i plus b times e top enclose j plus c times f top enclose k

m. top enclose u equals m a top enclose i plus m b top enclose j plus m c top enclose k

top enclose u plus top enclose v equals open parentheses a plus d close parentheses top enclose i plus open parentheses b plus e close parentheses top enclose j plus open parentheses c plus f close parentheses top enclose k

Pada soal diketahui:

top enclose a equals top enclose i plus 3 top enclose j minus 2 top enclose k top enclose a equals open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses 

top enclose b equals 4 top enclose i minus 2 top enclose j plus 4 top enclose k top enclose b equals open parentheses table row 4 row cell negative 2 end cell row 4 end table close parentheses

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 2 top enclose a space plus space top enclose b right parenthesis times left parenthesis top enclose a minus 2 top enclose b right parenthesis end cell equals cell open parentheses 2 open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses plus open parentheses table row 4 row cell negative 2 end cell row 4 end table close parentheses close parentheses times open parentheses open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses minus 2 open parentheses table row 4 row cell negative 2 end cell row 4 end table close parentheses close parentheses end cell row blank equals cell open parentheses open parentheses table row 2 row 6 row cell negative 4 end cell end table close parentheses plus open parentheses table row 4 row cell negative 2 end cell row 4 end table close parentheses close parentheses times open parentheses open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses minus open parentheses table row 8 row cell negative 4 end cell row 16 end table close parentheses close parentheses end cell row blank equals cell open parentheses table row 6 row 4 row 0 end table close parentheses times open parentheses table row cell negative 7 end cell row 7 row cell negative 18 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 6 times open parentheses negative 7 close parentheses end cell row cell 4 times 7 end cell row cell 0 times open parentheses negative 18 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 42 end cell row 28 row 0 end table close parentheses end cell end table 

Sehingga, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 top enclose a space plus space top enclose b right parenthesis times left parenthesis top enclose a minus 2 top enclose b right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals minus end table 42 top enclose i plus 28 top enclose j 

Jadi, hasil dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 top enclose a space plus space top enclose b right parenthesis times left parenthesis top enclose a minus 2 top enclose b right parenthesis end cell end table adalah 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 42 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose i 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 28 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose j end cell end table

164

5.0 (2 rating)

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