Diketahui vektor-vektor, ,, , dan, . Hitunglah:, d., searah, .,

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PERTANYAAN :

Diketahui vektor-vektor a with rightwards arrow on top equals i with rightwards arrow on top minus 2 j with rightwards arrow on top plus 3 k with rightwards arrow on topb with rightwards arrow on top equals 3 i with rightwards arrow on top minus j with rightwards arrow on top plus 3 k with rightwards arrow on top, dan c with rightwards arrow on top equals negative i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 5 k with rightwards arrow on top. Hitunglah:space

d. e with rightwards arrow on top searah open parentheses a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top close parentheses.space 

Table of Contents

Jawaban

 e with rightwards arrow on top searah open parentheses a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top close parentheses adalah fraction numerator 5 over denominator square root of 51 end fraction i with rightwards arrow on top minus fraction numerator 5 over denominator square root of 51 end fraction j with rightwards arrow on top plus fraction numerator 1 over denominator square root of 51 end fraction k with rightwards arrow on top.space


Pembahasan

Jawaban yang benar untuk pertanyaan d adalah fraction numerator 5 over denominator square root of 51 end fraction i with rightwards arrow on top minus fraction numerator 5 over denominator square root of 51 end fraction j with rightwards arrow on top plus fraction numerator 1 over denominator square root of 51 end fraction k with rightwards arrow on top.space 

Ingat.space

  • Untuk penjumlahan dua vektor atau lebih, dilakukan dengan menjumlahkan elemen-elemen yang sejenis.space
  • Untuk pengurangan dua vektor atau lebih, dilakukan dengan mengurangi elemen-elemen yang sejenis.space
  • Vektor satuan dari a with rightwards arrow on top equals x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top yaitu:space 

e with rightwards arrow on top equals fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction equals fraction numerator x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top over denominator square root of x squared plus y squared plus z squared end root end fractionspace 

Sehingga a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top dapat ditentukan sebagai berikut.space

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell open parentheses i with rightwards arrow on top minus 2 j with rightwards arrow on top plus 3 k with rightwards arrow on top close parentheses plus open parentheses 3 i with rightwards arrow on top minus j with rightwards arrow on top plus 3 k with rightwards arrow on top close parentheses minus open parentheses negative i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 5 k with rightwards arrow on top close parentheses end cell row blank equals cell 5 i with rightwards arrow on top minus 5 j with rightwards arrow on top plus k with rightwards arrow on top end cell end tablespace 

 straight e with rightwards arrow on top searah open parentheses straight a with rightwards arrow on top plus straight b with rightwards arrow on top minus straight c with rightwards arrow on top close parentheses adalahspace 

table attributes columnalign right center left columnspacing 0px end attributes row cell e with rightwards arrow on top end cell equals cell fraction numerator a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 5 i with rightwards arrow on top minus 5 j with rightwards arrow on top plus k with rightwards arrow on top over denominator square root of 5 squared plus open parentheses negative 5 close parentheses squared plus 1 squared end root end fraction end cell row blank equals cell fraction numerator 5 i with rightwards arrow on top minus 5 j with rightwards arrow on top plus k with rightwards arrow on top over denominator square root of 25 plus 25 plus 1 end root end fraction end cell row blank equals cell fraction numerator 5 i with rightwards arrow on top minus 5 j with rightwards arrow on top plus k with rightwards arrow on top over denominator square root of 51 end fraction end cell row blank equals cell fraction numerator 5 over denominator square root of 51 end fraction i with rightwards arrow on top minus fraction numerator 5 over denominator square root of 51 end fraction j with rightwards arrow on top plus fraction numerator 1 over denominator square root of 51 end fraction k with rightwards arrow on top end cell end tablespace 

Dengan demikian, e with rightwards arrow on top searah open parentheses a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top close parentheses adalah fraction numerator 5 over denominator square root of 51 end fraction i with rightwards arrow on top minus fraction numerator 5 over denominator square root of 51 end fraction j with rightwards arrow on top plus fraction numerator 1 over denominator square root of 51 end fraction k with rightwards arrow on top.space


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