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Diketahui a = ⎝ ⎛ ​ 4 x y ​ ⎠ ⎞ ​ , b = ⎝ ⎛ ​ − 1 2 6 ​ ⎠ ⎞ ​ dan c = ⎝ ⎛ ​ 4 − 1 − 3 ​ ⎠ ⎞ ​ . Jika vektor a dan b saling tegak lurus, maka a . c = ....

Diketahui  dan . Jika vektor  dan  saling tegak lurus, maka

  1. 2

  2. 4

  3. 6

  4. 12

  5. 14

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Pembahasan

Karena vektor dan saling tegak lurus, maka Kemudian didapat bahwa

Karena vektor begin mathsize 14px style straight a with rightwards arrow on top end style dan begin mathsize 14px style straight b with rightwards arrow on top end style saling tegak lurus, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top space. space straight b with rightwards arrow on top end cell equals 0 row cell open parentheses table row 4 row straight x row straight y end table close parentheses space. space open parentheses table row cell negative 1 end cell row 2 row 6 end table close parentheses end cell equals 0 row cell 4 left parenthesis negative 1 right parenthesis plus straight x left parenthesis 2 right parenthesis plus straight y left parenthesis 6 right parenthesis end cell equals cell 0 space end cell row cell negative 4 plus 2 straight x plus 6 straight y end cell equals cell 0 space end cell row cell 2 straight x plus 6 straight y end cell equals cell 4 space end cell row cell straight x plus 3 straight y end cell equals 2 end table end style 

Kemudian didapat bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top space. space straight c with rightwards arrow on top end cell equals cell open parentheses table row 4 row straight x row straight y end table close parentheses space. space open parentheses table row 4 row cell negative 1 end cell row cell negative 3 end cell end table close parentheses end cell row blank equals cell 4 left parenthesis 4 right parenthesis plus straight x left parenthesis negative 1 right parenthesis plus straight y left parenthesis negative 3 right parenthesis space end cell row blank equals cell 16 minus straight x minus 3 straight y space end cell row blank equals cell 16 minus left parenthesis straight x plus 3 straight y right parenthesis space end cell row blank equals cell 16 minus 2 space end cell row blank equals 14 end table end style 

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