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Pertanyaan

Diketahui vektor-vektor a = ( 3 5 ​ ) , b = ( 2 1 ​ ) ,dan c = ( − 4 8 ​ ) . Maka hitunglah vektor 2 a − b + 2 1 ​ c .

Diketahui vektor-vektor , , dan . Maka hitunglah vektor .space 

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A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

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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 a 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 cell b 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 cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 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 table row 2 row 13 end table close parentheses end cell end table.

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Pembahasan

Jika terdapat vektor dan skalar , maka perkalian vektor dengan skalar adalah: Diketahui , ,dan . Maka vektor adalah: Jadi, .

Jika terdapat vektor a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dan skalar k, maka perkalian vektor dengan skalar adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell k a with rightwards arrow on top end cell equals cell k open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell k a subscript 1 end cell row cell k a subscript 2 end cell end table close parentheses end cell end table 

Diketahui a with rightwards arrow on top equals open parentheses table row 3 row 5 end table close parentheses, b with rightwards arrow on top equals open parentheses table row 2 row 1 end table close parentheses, dan c with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 8 end table close parentheses. Maka vektor 2 italic a with rightwards arrow on top minus sign italic b with rightwards arrow on top plus 1 half italic c with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 a with rightwards arrow on top minus b with rightwards arrow on top plus 1 half c with rightwards arrow on top end cell row blank equals cell 2 open parentheses table row 3 row 5 end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses plus 1 half open parentheses table row cell negative 4 end cell row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 times 3 end cell row cell 2 times 5 end cell end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses plus open parentheses table row cell fraction numerator negative 4 over denominator 2 end fraction end cell row cell 8 over 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row 10 end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses plus open parentheses table row cell negative 2 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 6 minus 2 plus open parentheses negative 2 close parentheses end cell row cell 10 minus 1 plus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row 13 end table close parentheses end cell end table 

Jadi, 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 a 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 cell b 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 cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 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 table row 2 row 13 end table close parentheses end cell end table.

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Diketahui vektor p ​ = ( 3 4 ​ ) , vektor q ​ = ( 5 − 1 ​ ) , dan vektor r = ( − 2 6 ​ ) . Tentukan: b) p ​ + 2 q ​ − 3 r

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