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Diketahui A ( x , 7 , 0 ) , B ( 6 , 10 , − 6 ) ,dan C ( 1 , 9 , 0 ) agar AB ⊥ AC , maka nilai x = …

Diketahui , dan agar , maka nilai 

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

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Pembahasan

Dari soal diketahui Maka Karena maka Jadi, nilai atau

Dari soal diketahui

straight A left parenthesis straight x comma 7 comma 0 right parenthesis straight B left parenthesis 6 comma 10 comma negative 6 right parenthesis straight C open parentheses 1 comma 9 comma 0 close parentheses    

Maka  

table attributes columnalign right center left columnspacing 0px end attributes row AB equals cell open parentheses 6 comma 10 comma negative 6 close parentheses minus open parentheses x comma 7 comma 0 close parentheses end cell row blank equals cell open parentheses 6 minus x comma 3 comma negative 6 close parentheses end cell row AC equals cell open parentheses 1 comma 9 comma 0 close parentheses minus open parentheses x comma 7 comma 0 close parentheses end cell row blank equals cell open parentheses 1 minus x comma 2 comma 0 close parentheses end cell end table 

Karena AB perpendicular AC maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AB times AC over denominator open vertical bar A B close vertical bar open vertical bar A C close vertical bar end fraction end cell equals cell cos space 90 end cell row cell fraction numerator AB times AC over denominator open vertical bar AB close vertical bar open vertical bar AC close vertical bar end fraction end cell equals 0 row cell AB times AC end cell equals 0 row cell open parentheses table row cell 6 minus straight x end cell row 3 row cell negative 6 end cell end table close parentheses open parentheses table row cell 1 minus straight x end cell row 2 row 0 end table close parentheses end cell equals 0 row cell 6 minus 7 straight x plus straight x squared plus 6 plus 0 end cell equals 0 row cell straight x squared minus 7 straight x plus 12 end cell equals 0 row cell open parentheses straight x minus 4 close parentheses open parentheses straight x minus 3 close parentheses end cell equals 0 row straight x equals cell 4 space atau space straight x equals 3 end cell end table 

Jadi, nilai bold italic x bold equals bold 4 atau bold italic x bold equals bold 3  

 

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