Pertanyaan

Diketahui A ( 2 , 6 , − 5 ) , B ( − 1 , 3 , 7 ) , dan C ( 4 , − 1 , 8 ) . AB dan BC berturut-turut mewakili vektor u dan v . Tentukan: a. ( 2 u ) ⋅ v

Diketahui , , dan  dan  berturut-turut mewakili vektor  dan .

Tentukan:

a. space 

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 u with rightwards arrow on top close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell v 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 18 end table.

Pembahasan

Jika dan , maka adalah: Vektor Posisiadalah vektor yang berpangkal di pusat koordinat dan berujung di suatu titik . Diketahui , , dan . Nilai vektor posisi akan sama dengan koordinat titik ujungnya, maka tentukan dan . a. Jadi, .

Jika 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 b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses, maka a with rightwards arrow on top times b with rightwards arrow on top adalah:

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

Vektor Posisi adalah vektor yang berpangkal di pusat koordinat open parentheses 0 comma space 0 close parentheses dan berujung di suatu titik open parentheses x comma space y close parentheses.

Diketahui straight A open parentheses 2 comma space 6 comma space minus 5 close parentheses, straight B open parentheses negative 1 comma space 3 comma space 7 close parentheses, dan straight C open parentheses 4 comma space minus 1 comma space 8 close parentheses.

Nilai vektor posisi akan sama dengan koordinat titik ujungnya, maka tentukan AB with rightwards arrow on top dan BC with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell b with rightwards arrow on top minus a with rightwards arrow on top end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 1 end cell row 3 row 7 end table close parentheses minus open parentheses table row 2 row 6 row cell negative 5 end cell end table close parentheses end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 1 minus 2 end cell row cell 3 minus 6 end cell row cell 7 plus 5 end cell end table close parentheses end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses end cell row cell BC with rightwards arrow on top end cell equals cell c with rightwards arrow on top minus b with rightwards arrow on top end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row 4 row cell negative 1 end cell row 8 end table close parentheses minus open parentheses table row cell negative 1 end cell row 3 row 7 end table close parentheses end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row cell 4 plus 1 end cell row cell negative 1 minus 3 end cell row cell 8 minus 7 end cell end table close parentheses end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses end cell end table   

a. open parentheses 2 u with rightwards arrow on top close parentheses times v with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 u with rightwards arrow on top close parentheses times v with rightwards arrow on top end cell equals cell 2 open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses times open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell row cell negative 6 end cell row 24 end table close parentheses times open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses negative 6 close parentheses times 5 plus open parentheses negative 6 close parentheses times open parentheses negative 4 close parentheses plus 24 times 1 end cell row blank equals cell negative 30 plus 24 plus 24 end cell row blank equals 18 end table 

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 u with rightwards arrow on top close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell v 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 18 end table.

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