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Jika a=3i+4j​−5k, b=i+2j​−3k dan c=−i+2j​+32​k, maka vektor satuan d=a−2b+3c adalah ...

Pertanyaan

Jika straight a with rightwards arrow on top equals 3 straight i with rightwards arrow on top plus 4 straight j with rightwards arrow on top minus 5 straight k with rightwards arrow on top, straight b with rightwards arrow on top equals straight i with rightwards arrow on top plus 2 straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top dan straight c with rightwards arrow on top equals negative straight i with rightwards arrow on top plus 2 straight j with rightwards arrow on top plus 2 over 3 straight k with rightwards arrow on top, maka vektor satuan straight d with rightwards arrow on top equals straight a with rightwards arrow on top minus 2 straight b with rightwards arrow on top plus 3 straight c with rightwards arrow on top adalah ...

  1. 2 over 7 straight i with rightwards arrow on top minus 6 over 7 straight j with rightwards arrow on top minus 3 over 7 straight k with rightwards arrow on top

  2. negative 2 over 7 straight i with rightwards arrow on top plus 6 over 7 straight j with rightwards arrow on top plus 3 over 7 straight k with rightwards arrow on top

  3. negative 2 straight i with rightwards arrow on top plus 6 straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top

  4. 2 straight i with rightwards arrow on top minus 6 straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top

  5. negative 2 over 5 straight i with rightwards arrow on top plus 6 over 5 straight j with rightwards arrow on top plus 3 over 5 straight k with rightwards arrow on top

Pembahasan:

Vektor satuan dari vektor tiga dimensi straight a with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 end cell row cell straight a subscript 2 end cell row cell straight a subscript 3 end cell end table close parentheses adalah sebagai berikut.

fraction numerator straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction equals fraction numerator open parentheses straight a subscript 1 comma space straight a subscript 2 comma space straight a subscript 3 close parentheses over denominator square root of straight a subscript 1 squared plus straight a subscript 2 squared plus straight a subscript 3 squared end root end fraction.

Sebelum mencari vektor satuan dari straight d with rightwards arrow on top, hitunglah operasi vektornya terlebih dahulu, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight d with rightwards arrow on top end cell equals cell straight a with rightwards arrow on top minus 2 straight b with rightwards arrow on top plus 3 straight c with rightwards arrow on top end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 3 row 4 row cell negative 5 end cell end table close parentheses minus 2 open parentheses table row 1 row 2 row cell negative 3 end cell end table close parentheses plus 3 open parentheses table row cell negative 1 end cell row 2 row cell begin inline style 2 over 3 end style end cell end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 3 row 4 row cell negative 5 end cell end table close parentheses minus open parentheses table row 2 row 4 row cell negative 6 end cell end table close parentheses plus open parentheses table row cell negative 3 end cell row 6 row 2 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row cell 3 minus 2 minus 3 end cell row cell 4 minus 4 plus 6 end cell row cell negative 5 plus 6 plus 2 end cell end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row cell negative 2 end cell row 6 row 3 end table close parentheses end cell end table 

Selanjutnya, vektor satuan straight d with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d with rightwards arrow on top over denominator open vertical bar straight d with rightwards arrow on top close vertical bar end fraction end cell equals cell fraction numerator open parentheses negative 2 comma space 6 comma space 3 close parentheses over denominator square root of open parentheses negative 2 close parentheses squared plus 6 squared plus 3 squared end root end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 comma space 6 comma space 3 close parentheses over denominator square root of 4 plus 36 plus 9 end root end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 comma space 6 comma space 3 close parentheses over denominator square root of 49 end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 comma space 6 comma space 3 close parentheses over denominator 7 end fraction end cell row blank equals cell open parentheses negative 2 over 7 comma space 6 over 7 comma space 3 over 7 close parentheses end cell row blank equals cell negative 2 over 7 straight i with rightwards arrow on top plus 6 over 7 straight j with rightwards arrow on top plus 3 over 7 straight k with rightwards arrow on top end cell end table

Dengan demikian, jawaban yang benar adalah B.

Jawaban terverifikasi

Dijawab oleh:

R. Hajrianti

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 07 Oktober 2021

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