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Pertanyaan

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 parenthesesAB with rightwards arrow on top dan BC with rightwards arrow on top berturut-turut mewakili vektor u with rightwards arrow on top dan v with rightwards arrow on top.

Tentukan:

b. u with rightwards arrow on top times open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses space 

A. Acfreelance

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u with rightwards arrow on top 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 open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses 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 171 end table.

Pembahasan

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   

b. u with rightwards arrow on top times open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u with rightwards arrow on top times open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses end cell row blank equals cell u with rightwards arrow on top times u with rightwards arrow on top plus u with rightwards arrow on top times v with rightwards arrow on top end cell row blank equals cell 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 cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses plus 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 open parentheses negative 3 close parentheses squared plus open parentheses negative 3 close parentheses squared plus 12 squared close parentheses plus open parentheses open parentheses negative 3 close parentheses times 5 plus open parentheses negative 3 close parentheses times open parentheses negative 4 close parentheses plus 12 times 1 close parentheses end cell row blank equals cell 162 plus 9 end cell row blank equals 171 end table 

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u with rightwards arrow on top 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 open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses 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 171 end table.

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