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Diketahui koordinat P(-1,1,-1), Q(–1,0,–1) dan R(0,1,0). Vektor PQ ​ mewakili a dan vektor QR ​ mewakili b . Hasil operasi vektor 2 1 ​ a + b = ....

Diketahui koordinat P(-1,1,-1), Q(–1,0,–1) dan R(0,1,0).  Vektor  mewakili  dan vektor  mewakili . Hasil operasi vektor

  1. begin mathsize 14px style straight i with rightwards arrow on top plus 1 half straight j with rightwards arrow on top plus straight k with rightwards arrow on top end style 

  2. begin mathsize 14px style straight i with rightwards arrow on top minus 1 half straight j with rightwards arrow on top plus straight k with rightwards arrow on top end style 

  3. begin mathsize 14px style straight i with rightwards arrow on top plus 1 half straight j with rightwards arrow on top minus straight k with rightwards arrow on top end style 

  4. begin mathsize 14px style negative straight i with rightwards arrow on top plus 1 half straight j with rightwards arrow on top plus straight k with rightwards arrow on top end style 

  5. begin mathsize 14px style negative straight i with rightwards arrow on top minus 1 half straight j with rightwards arrow on top plus straight k with rightwards arrow on top end style 

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 begin mathsize 14px style 1 half straight a with rightwards arrow on top plus straight b with rightwards arrow on top equals straight i with rightwards arrow on top plus 1 half straight j with rightwards arrow on top plus straight k with rightwards arrow on top end style

Pembahasan

Dari (i) dan (ii) maka: Jadi

begin mathsize 14px style straight a with rightwards arrow on top equals PQ with rightwards arrow on top equals straight Q minus straight P equals open parentheses table row cell negative 1 end cell row 0 row cell negative 1 end cell end table close parentheses minus open parentheses table row cell negative 1 end cell row 1 row cell negative 1 end cell end table close parentheses equals open parentheses table row 0 row cell negative 1 end cell row 0 end table close parentheses straight b with rightwards arrow on top equals QR with rightwards arrow on top equals straight R minus straight Q equals open parentheses table row 0 row 1 row 0 end table close parentheses minus open parentheses table row cell negative 1 end cell row 0 row cell negative 1 end cell end table close parentheses equals open parentheses table row 1 row 1 row 1 end table close parentheses end style 

Dari (i) dan (ii) maka:

begin mathsize 14px style 1 half straight a with rightwards arrow on top plus straight b with rightwards arrow on top equals 1 half open parentheses table row 0 row cell negative 1 end cell row 0 end table close parentheses plus open parentheses table row 1 row 1 row 1 end table close parentheses plus open parentheses table row 1 row cell negative 1 half end cell row 0 end table close parentheses plus open parentheses table row 1 row 1 row 1 end table close parentheses equals open parentheses table row 1 row cell 1 half end cell row 1 end table close parentheses end style

Jadi begin mathsize 14px style 1 half straight a with rightwards arrow on top plus straight b with rightwards arrow on top equals straight i with rightwards arrow on top plus 1 half straight j with rightwards arrow on top plus straight k with rightwards arrow on top end style

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Diketahui vektor-vektor a = i + 2 j ​ − 3 k , b = 3 i + 5 j ​ , c = − 2 i − 4 j ​ + k ,dan vektor u = 2 a + b − c . Vektor dapat dijabarkan menjadi....

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