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Pertanyaan

Diketahui m = ⎝ ⎛ ​ 4 3 − 2 ​ ⎠ ⎞ ​ dan n = ⎝ ⎛ ​ 2 1 a ​ ⎠ ⎞ ​ . Jika panjang vektor p ​ = 2 m + n adalah 5 6 ​ tentukan nilai .

Diketahui . Jika panjang vektor  adalah  tentukan nilai a.

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L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

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Pembahasan

Sekarang, kita hitung panjang . sehingga, Jadi, .

p with rightwards arrow on top equals 2 m with rightwards arrow on top plus n with rightwards arrow on top space space equals 2 open parentheses table row 4 row 3 row cell negative 2 end cell end table close parentheses plus open parentheses table row 2 row cell negative 1 end cell row a end table close parentheses space space equals open parentheses table row 8 row 6 row cell negative 4 end cell end table close parentheses plus open parentheses table row 2 row cell negative 1 end cell row a end table close parentheses space space equals open parentheses table row 10 row 5 row cell negative 4 plus a end cell end table close parentheses 

Sekarang, kita hitung panjang p with rightwards arrow on top.

space space space space space space space space space space open vertical bar p with rightwards arrow on top close vertical bar equals square root of 10 squared plus 5 squared plus open parentheses negative 4 plus a close parentheses squared end root space space space space space space space 5 square root of 6 equals square root of 100 plus 25 plus open parentheses negative 4 plus a close parentheses squared end root space space space open parentheses 5 square root of 6 close parentheses squared equals 125 plus open parentheses negative 4 plus a close parentheses squared space space space space space space space space 150 equals 125 plus open parentheses negative 4 plus a close parentheses squared open parentheses negative 4 plus a close parentheses squared equals 25 space space space minus 4 plus a equals plus-or-minus 5 

sehingga,

negative 4 plus a equals 5 space space space space space space space atau space space space space space minus 4 plus a equals negative 5 space space space space space space space space space a equals 9 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 a equals negative 1 

Jadi, a equals 9 space atau space a equals negative 1

 

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