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Diketahui vektor u = 3 i + 2 j ​ + 2 k dan v = i + j ​ − 4 k . Tentukan : b. panjang vektor u , v dan u + 2 v

Diketahui vektor  dan . Tentukan :

b. panjang vektor  dan 

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H. Firmansyah

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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Pembahasan

Perhatikan panjang vektor panjang vektor panjang vektor

Perhatikan 

  • panjang vektor begin mathsize 14px style u with rightwards arrow on top end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar u with rightwards arrow on top close vertical bar end cell equals cell square root of 3 squared plus 2 squared plus 2 squared end root end cell row blank equals cell square root of 9 plus 4 plus 4 end root end cell row blank equals cell square root of 17 end cell end table end style

  • panjang vektor begin mathsize 14px style v with rightwards arrow on top end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals cell square root of 1 squared plus 1 squared plus open parentheses negative 4 close parentheses squared end root end cell row blank equals cell square root of 1 plus 1 plus 16 end root end cell row blank equals cell square root of 18 end cell row blank equals cell 3 square root of 2 end cell end table end style

  • panjang vektor

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top plus 2 v with rightwards arrow on top end cell equals cell open parentheses table row 3 row 2 row 2 end table close parentheses plus 2 open parentheses table row 1 row 1 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 row 4 row cell negative 6 end cell end table close parentheses end cell row blank equals cell 5 i with rightwards arrow on top plus 4 j with rightwards arrow on top minus 6 k with rightwards arrow on top end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar u with rightwards arrow on top plus 2 v with rightwards arrow on top close vertical bar end cell equals cell square root of 5 squared plus 4 squared plus open parentheses negative 6 close parentheses squared end root end cell row blank equals cell square root of 25 plus 16 plus 36 end root end cell row blank equals cell square root of 77 end cell end table end style 

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Diketahui vektor-vektor a = i − 2 j ​ + 3 k , b = 3 i − j ​ + 3 k , dan c = − i + 2 j ​ + 5 k . Hitunglah: a. ∣ ∣ ​ a − c ∣ ∣ ​ ,

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