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Pertanyaan

Diketahui a = ( 3 2 ​ ) , b = ( − 8 9 ​ ) dan c = ( 12 13 ​ ) . Jika d = a + b + c maka panjang vektor d = ...

Diketahui  dan . Jika  maka panjang vektor  

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R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

jawaban yang tepat adalah E.

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Pembahasan

Diketahui , , dan . Ingat! Pada vektor, jika dan maka . Jika vektor atau maka panjang vektor adalah . Sehingga: Jadi, jawaban yang tepat adalah E.

Diketahui a with rightwards arrow on top equals open parentheses table row 3 row 2 end table close parenthesesb with rightwards arrow on top equals open parentheses table row cell negative 8 end cell row 9 end table close parenthesesc with rightwards arrow on top equals open parentheses table row 12 row 13 end table close parentheses dan d with rightwards arrow on top equals a with rightwards arrow on top plus b with rightwards arrow on top plus c with rightwards arrow on top.

Ingat!

  • Pada vektor, 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 plus b with rightwards arrow on top equals open parentheses table row cell a subscript 1 plus b subscript 1 end cell row cell a subscript 2 plus b subscript 2 end cell end table close parentheses.
  • Jika 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 atau a with rightwards arrow on top equals left parenthesis a subscript 1 comma space a subscript 2 right parenthesis maka panjang vektor a with rightwards arrow on top adalah open vertical bar a with rightwards arrow on top close vertical bar equals square root of a subscript 1 squared plus a subscript 2 squared end root.

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell d with rightwards arrow on top end cell equals cell a with rightwards arrow on top plus b with rightwards arrow on top plus c with rightwards arrow on top end cell row blank equals cell open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses plus c with rightwards arrow on top end cell row blank equals cell open parentheses table row 3 row 2 end table close parentheses plus open parentheses table row cell negative 8 end cell row 9 end table close parentheses plus open parentheses table row 12 row 13 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 plus left parenthesis negative 8 right parenthesis end cell row cell 2 plus 9 end cell end table close parentheses plus open parentheses table row 12 row 13 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 end cell row 11 end table close parentheses plus open parentheses table row 12 row 13 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 plus 12 end cell row cell 11 plus 13 end cell end table close parentheses end cell row blank equals cell open parentheses table row 7 row 24 end table close parentheses end cell row blank blank blank row cell open vertical bar d with rightwards arrow on top close vertical bar end cell equals cell square root of 7 squared plus 24 squared end root end cell row blank equals cell square root of 49 plus 576 end root end cell row blank equals cell square root of 625 end cell row blank equals cell 25 space satuan space panjang end cell end table 

Jadi, jawaban yang tepat adalah E.

Latihan Bab

Pengertian dan Operasi Vektor I

Operasi Vektor II

Kedudukan Vektor

Aljabar Vektor I

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