Pertanyaan

Diketahui vektor u = ⎝ ⎛ 4 3 − 8 ⎠ ⎞ dan v = ⎝ ⎛ a − 5 − 2 ⎠ ⎞ . Jika hasil u ⋅ v = − 11 , tentukan: b. Hasil v ⋅ ( u − v )

Diketahui vektor $u = ⎝ ⎛ 43 - 8 ⎠ ⎞ dan v = ⎝ ⎛ a - 5 - 2 ⎠ ⎞ .$ Jika hasil $u \cdot v = - 11,$ tentukan:

b. Hasil $v \cdot (u - v)$

A. Tegar

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Jawaban terverifikasi

Jawaban

hasilnya adalah

Pembahasan

Perhatikan penghitungan berikut! Jadi, hasilnya adalah

Perhatikan penghitungan berikut!

$begin mathsize 14px style u with rightwards arrow on top times v with rightwards arrow on top space space space space space equals open parentheses table row 4 row 3 row cell negative 8 end cell end table close parentheses times open parentheses table row a row cell negative 5 end cell row cell negative 2 end cell end table close parentheses minus 11 space space space space space equals 4 a minus 15 plus 16 minus 11 space space space space space equals 4 a plus 1 minus 11 minus 1 equals 4 a minus 12 space space space space space equals 4 a fraction numerator negative 12 over denominator 4 end fraction space space space space equals a minus 3 space space space space space space space equals a v with rightwards arrow on top times open parentheses u with rightwards arrow on top minus v with rightwards arrow on top close parentheses equals open parentheses table row a row cell negative 5 end cell row cell negative 2 end cell end table close parentheses times open parentheses open parentheses table row 4 row 3 row cell negative 8 end cell end table close parentheses minus open parentheses table row a row cell negative 5 end cell row cell negative 2 end cell end table close parentheses close parentheses v with rightwards arrow on top times open parentheses u with rightwards arrow on top minus v with rightwards arrow on top close parentheses equals open parentheses table row a row cell negative 5 end cell row cell negative 2 end cell end table close parentheses times open parentheses table row cell 4 minus a end cell row 8 row cell negative 6 end cell end table close parentheses v with rightwards arrow on top times open parentheses u with rightwards arrow on top minus v with rightwards arrow on top close parentheses equals a left parenthesis 4 minus a right parenthesis plus left parenthesis negative 5 right parenthesis left parenthesis 8 right parenthesis plus left parenthesis negative 2 right parenthesis left parenthesis negative 6 right parenthesis v with rightwards arrow on top times open parentheses u with rightwards arrow on top minus v with rightwards arrow on top close parentheses equals open parentheses negative 3 close parentheses left parenthesis 4 minus open parentheses negative 3 close parentheses right parenthesis plus left parenthesis negative 5 right parenthesis left parenthesis 8 right parenthesis plus left parenthesis negative 2 right parenthesis left parenthesis negative 6 right parenthesis v with rightwards arrow on top times open parentheses u with rightwards arrow on top minus v with rightwards arrow on top close parentheses equals negative 21 minus 40 plus 12 v with rightwards arrow on top times open parentheses u with rightwards arrow on top minus v with rightwards arrow on top close parentheses equals negative 49 end style$

Jadi, hasilnya adalah