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Pertanyaan

Jika vektor a with rightwards arrow on top equals x i minus 4 j plus 8 k tegak lurus vektor b with rightwards arrow on top equals 2 x i plus 2 x j minus 3 k, maka nilai x yang memenuhi adalah ...

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

nilai x yang memenuhi adalah x equals 6 atau x equals negative 2.

Pembahasan

Ingat, jika vektor a with rightwards arrow on top tegak lurus b with rightwards arrow on top, maka 

a with rightwards arrow on top. b with rightwards arrow on top equals 0 

Pada soal kita, a with rightwards arrow on top equals open parentheses table row x row cell negative 4 end cell row 8 end table close parentheses space space comma space space space b with rightwards arrow on top equals open parentheses table row cell 2 x end cell row cell 2 x end cell row cell negative 3 end cell end table close parentheses, maka

a with rightwards arrow on top. b with rightwards arrow on top equals 0 space space space rightwards arrow space x.2 x plus open parentheses negative 4 close parentheses.2 x plus 8. open parentheses negative 3 close parentheses equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 x squared minus 8 x minus 24 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space x squared minus 4 x minus 12 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses x minus 6 close parentheses open parentheses x plus 2 close parentheses equals 0 

Pembuat nol:

x minus 6 equals 0 space space space space space a t a u space space space space space space space space space space x plus 2 equals 0 space space space space space space x equals 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space x equals negative 2 

Jadi, nilai x yang memenuhi adalah x equals 6 atau x equals negative 2.

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