Diberikan vektor . Jika vektor tegak lurus vektor...

Diberikan vektor $begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row p row 2 row cell negative 1 end cell end table close parentheses comma space b with rightwards arrow on top equals open parentheses table row 4 row cell negative 3 end cell row 6 end table close parentheses comma space dan space c with rightwards arrow on top equals open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses end style$ . Jika vektor $begin mathsize 14px style a with rightwards arrow on top end style$ tegak lurus vektor $begin mathsize 14px style b with rightwards arrow on top end style$ , maka hasil dari $begin mathsize 14px style open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses times open parentheses 2 c with rightwards arrow on top close parentheses end style$ adalah ....

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Jawaban:

Jika vektor $begin mathsize 14px style a with rightwards arrow on top end style$ tegak lurus vektor $begin mathsize 14px style b with rightwards arrow on top end style$ , maka $begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top equals 0 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals 0 row cell open parentheses table row p row 2 row cell negative 1 end cell end table close parentheses times open parentheses table row 4 row cell negative 3 end cell row 6 end table close parentheses end cell equals 0 row cell 4 p plus 2 open parentheses negative 3 close parentheses plus open parentheses negative 1 close parentheses open parentheses 6 close parentheses end cell equals 0 row cell 4 p minus 6 minus 6 end cell equals 0 row cell 4 p minus 12 end cell equals 0 row cell 4 p end cell equals 12 row p equals 3 end table end style$

Sehingga vektor $begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses end style$

Menentukan hasil dari $begin mathsize 14px style open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses times open parentheses 2 c with rightwards arrow on top close parentheses end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses times open parentheses 2 c with rightwards arrow on top close parentheses end cell equals cell open parentheses open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses minus open parentheses table row 4 row cell negative 3 end cell row 6 end table close parentheses close parentheses times open parentheses 2 open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 5 row cell negative 7 end cell end table close parentheses times open parentheses table row 4 row cell negative 2 end cell row 6 end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses 4 close parentheses plus 5 open parentheses negative 2 close parentheses plus open parentheses negative 7 close parentheses open parentheses 6 close parentheses end cell row blank equals cell negative 4 plus open parentheses negative 10 close parentheses plus open parentheses negative 42 close parentheses end cell row blank equals cell negative 56 end cell end table end style$

Jadi, hasil dari $begin mathsize 14px style open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses times open parentheses 2 c with rightwards arrow on top close parentheses end style$ adalah $begin mathsize 14px style negative 56 end style$ .

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