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Diketahui , , dan . Tentukan vektor-vektor berikut. f.

Pertanyaan

Diketahui begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 2 row cell negative 3 end cell end table close parentheses end stylebegin mathsize 14px style b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 5 end table close parentheses end style, dan begin mathsize 14px style c with rightwards arrow on top equals open parentheses table row 6 row 4 end table close parentheses end style.

Tentukan vektor-vektor berikut.

f. begin mathsize 14px style 10 a with rightwards arrow on top plus 4 b with rightwards arrow on top plus c with rightwards arrow on top end style 

Pembahasan Soal:

Gunakan konsep pekalian skalar dengan vektor dan penjumlahan dua vektor sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell k m with rightwards arrow on top end cell equals cell k open parentheses table row e row f end table close parentheses equals open parentheses table row cell k times e end cell row cell k times f end cell end table close parentheses end cell row cell m with rightwards arrow on top plus n with rightwards arrow on top end cell equals cell open parentheses table row e row f end table close parentheses plus open parentheses table row g row h end table close parentheses equals open parentheses table row cell e plus g end cell row cell f plus h end cell end table close parentheses end cell end table end style  

Perhatikan perhitungan sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell 10 a with rightwards arrow on top plus 4 b with rightwards arrow on top plus c with rightwards arrow on top end cell equals cell 10 open parentheses table row 2 row cell negative 3 end cell end table close parentheses plus 4 open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus open parentheses table row 6 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 10 cross times 2 end cell row cell 10 cross times open parentheses negative 3 close parentheses end cell end table close parentheses plus open parentheses table row cell 4 cross times open parentheses negative 3 close parentheses end cell row cell 4 cross times 5 end cell end table close parentheses plus open parentheses table row 6 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 20 row cell negative 30 end cell end table close parentheses plus open parentheses table row cell negative 12 end cell row 20 end table close parentheses plus open parentheses table row 6 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 20 plus open parentheses negative 12 close parentheses plus 6 end cell row cell negative 30 plus 20 plus 4 end cell end table close parentheses end cell row cell 10 a with rightwards arrow on top plus 4 b with rightwards arrow on top plus c with rightwards arrow on top end cell equals cell open parentheses table row 14 row cell negative 6 end cell end table close parentheses end cell end table end style   

Jadi, diperoleh begin mathsize 14px style 10 a with rightwards arrow on top plus 4 b with rightwards arrow on top plus c with rightwards arrow on top equals open parentheses table row 14 row cell negative 6 end cell end table close parentheses end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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