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Diketahui vektor: a → = i → − x j → ​ + 3 k ⇀ b → = 2 i → + j → ​ − k ⇀ c → = i → + 3 j → ​ + 2 k ⇀ JIka a tegak lurus b ⇀ maka hasil dari a × ( b + c ) adalah ...

Diketahui vektor:

  

JIka  tegak lurus  maka hasil dari    adalah ...
 

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, maka didapat . Jadi nilai

begin mathsize 14px style a with rightwards arrow on top space tegak space lurus space b with rightwards arrow on top end style, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals 0 row cell left parenthesis i with rightwards arrow on top short dash x j with rightwards arrow on top plus stack 3 k with rightwards arrow on top right parenthesis times left parenthesis 2 i with rightwards arrow on top plus j with rightwards arrow on top minus k with rightwards arrow on top right parenthesis end cell equals 0 row cell 2 minus x minus 3 end cell equals 0 row cell negative x minus 1 end cell equals 0 row x equals cell negative 1 end cell end table

didapat a with rightwards arrow on top equals i with rightwards arrow on top plus j with rightwards arrow on top plus 3 k with rightwards arrow on top.

Jadi nilai

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top cross times left parenthesis b with rightwards arrow on top plus c with rightwards arrow on top right parenthesis end cell equals cell left parenthesis i with rightwards arrow on top plus j with rightwards arrow on top plus 3 k with rightwards arrow on top right parenthesis cross times left parenthesis 2 i with rightwards arrow on top plus j with rightwards arrow on top minus k with rightwards arrow on top plus i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 2 k with rightwards arrow on top right parenthesis end cell row blank equals cell left parenthesis i with rightwards arrow on top plus j with rightwards arrow on top plus 3 k with rightwards arrow on top right parenthesis cross times left parenthesis 3 i with rightwards arrow on top plus 4 j with rightwards arrow on top plus k with rightwards arrow on top right parenthesis end cell row blank equals cell left parenthesis 1 minus 12 right parenthesis i with rightwards arrow on top plus left parenthesis 9 minus 1 right parenthesis j with rightwards arrow on top plus left parenthesis 4 minus 3 right parenthesis k with rightwards arrow on top end cell row blank equals cell negative 11 i with rightwards arrow on top plus 8 j with rightwards arrow on top plus k with rightwards arrow on top end cell end table 

 

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