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Diketahui sebuah vektor a = − 2 i + j ​ + 2 k , maka vektor satuan a adalah ....

Diketahui sebuah vektor , maka vektor satuan  adalah ....

  1. begin mathsize 14px style 2 over 3 straight i with rightwards arrow on top plus 1 third straight j with rightwards arrow on top plus 2 over 3 straight k with rightwards arrow on top end style  

  2. begin mathsize 14px style 2 over 3 straight i with rightwards arrow on top minus 1 third straight j with rightwards arrow on top plus 2 over 3 straight k with rightwards arrow on top end style 

  3. begin mathsize 14px style negative 2 over 3 straight i with rightwards arrow on top plus 1 third straight j with rightwards arrow on top plus 2 over 3 straight k with rightwards arrow on top end style 

  4. begin mathsize 14px style negative 2 over 3 straight i with rightwards arrow on top minus 1 third straight j with rightwards arrow on top plus 2 over 3 straight k with rightwards arrow on top end style 

  5. begin mathsize 14px style negative 2 over 3 straight i with rightwards arrow on top plus 1 third straight j with rightwards arrow on top minus 2 over 3 straight k with rightwards arrow on top end style 

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Jawaban

vektor satuan adalah

vektor satuan begin mathsize 14px style straight a with rightwards arrow on top end style  adalah begin mathsize 14px style 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 negative 2 straight i with rightwards arrow on top plus straight j with rightwards arrow on top plus 2 straight k with rightwards arrow on top over denominator 3 end fraction equals negative 2 over 3 straight i with rightwards arrow on top plus 1 third straight j with rightwards arrow on top plus 2 over 3 straight k with rightwards arrow on top end style

Pembahasan

Ingat: Vektor satuan dinyatakan sebagai Pertama-tama dicari panjang terlebih dulu Jadi vektor satuan adalah

Ingat:

Vektor satuan undefined dinyatakan sebagai begin mathsize 14px style fraction numerator straight u with rightwards arrow on top over denominator open vertical bar straight u with rightwards arrow on top close vertical bar end fraction end style

  • Pertama-tama dicari panjang begin mathsize 14px style straight a with rightwards arrow on top end style terlebih dulu

begin mathsize 14px style open vertical bar straight a with rightwards arrow on top close vertical bar equals square root of open parentheses negative 2 squared close parentheses plus open parentheses 1 close parentheses squared plus open parentheses 2 close parentheses squared end root equals square root of 4 plus 1 plus 4 end root equals square root of 9 equals 3 end style

Jadi vektor satuan begin mathsize 14px style straight a with rightwards arrow on top end style  adalah begin mathsize 14px style 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 negative 2 straight i with rightwards arrow on top plus straight j with rightwards arrow on top plus 2 straight k with rightwards arrow on top over denominator 3 end fraction equals negative 2 over 3 straight i with rightwards arrow on top plus 1 third straight j with rightwards arrow on top plus 2 over 3 straight k with rightwards arrow on top end style

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Diketahui vektor u = ⎝ ⎛ ​ 2 1 ​ 4 3 ​ x ​ ⎠ ⎞ ​ dan v = ⎝ ⎛ ​ 4 1 ​ x y ​ ⎠ ⎞ ​ adalah vektor satuan. Panjang dari vektor p ​ = ⎝ ⎛ ​ x 2 3 ​ y ​ ⎠ ⎞ ​ adalah ....

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