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Pertanyaan

Diketahui vektor u = ( − 5 7 ​ ) dan v = ( 4 a ​ ) . Jika hasil u ⋅ v = − 6 , tentukan: a. nilai a b. hasil ( 2 u + 3 v ) ⋅ ( u − 2 v )

Diketahui vektor  dan . Jika hasil , tentukan:

a. nilai  

b. hasil  

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A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top right parenthesis times left parenthesis u with rightwards arrow on top minus 2 v with rightwards arrow on top right parenthesis 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 34 end table end style.

Pembahasan

Nilai adalah: Sehingga,hasil adalah: Jadi, .

Nilai size 14px a adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top times v with rightwards arrow on top end cell equals cell negative 6 end cell row cell open parentheses table row cell negative 5 end cell row 7 end table close parentheses times open parentheses table row 4 row a end table close parentheses end cell equals cell negative 6 end cell row cell open parentheses negative 5 close parentheses times 4 plus 7 a end cell equals cell negative 6 end cell row cell negative 20 plus 7 a end cell equals cell negative 6 end cell row cell 7 a end cell equals cell negative 6 plus 20 end cell row a equals cell 14 over 7 end cell row a equals 2 end table end style 

Sehingga, hasil begin mathsize 14px style open parentheses 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top close parentheses times open parentheses u with rightwards arrow on top minus 2 v with rightwards arrow on top close parentheses end style adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top right parenthesis times left parenthesis u with rightwards arrow on top minus 2 v with rightwards arrow on top right parenthesis end cell equals cell open parentheses 2 open parentheses table row cell negative 5 end cell row 7 end table close parentheses plus 3 open parentheses table row 4 row 2 end table close parentheses close parentheses times open parentheses open parentheses table row cell negative 5 end cell row 7 end table close parentheses minus 2 open parentheses table row 4 row 2 end table close parentheses close parentheses end cell row blank equals cell open parentheses open parentheses table row cell negative 10 end cell row 14 end table close parentheses plus open parentheses table row 12 row 6 end table close parentheses close parentheses times open parentheses open parentheses table row cell negative 5 end cell row 7 end table close parentheses minus open parentheses table row 8 row 4 end table close parentheses close parentheses end cell row blank equals cell open parentheses table row 2 row 20 end table close parentheses times open parentheses table row cell negative 13 end cell row 3 end table close parentheses end cell row blank equals cell 2 times open parentheses negative 13 close parentheses plus 20 times 3 end cell row blank equals cell negative 26 plus 60 end cell row blank equals 34 end table end style 

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top right parenthesis times left parenthesis u with rightwards arrow on top minus 2 v with rightwards arrow on top right parenthesis 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 34 end table end style.

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