Roboguru

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

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.

e. begin mathsize 14px style b with rightwards arrow on top plus 4 c with rightwards arrow on top plus a 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 b with rightwards arrow on top plus 4 c with rightwards arrow on top plus a with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus 4 open parentheses table row 6 row 4 end table close parentheses plus open parentheses table row 2 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus open parentheses table row cell 4 cross times 6 end cell row cell 4 cross times 4 end cell end table close parentheses plus open parentheses table row 2 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses plus open parentheses table row 24 row 16 end table close parentheses plus open parentheses table row 2 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 plus 24 plus 2 end cell row cell 5 plus 16 plus open parentheses negative 3 close parentheses end cell end table close parentheses end cell row cell b with rightwards arrow on top plus 4 c with rightwards arrow on top plus a with rightwards arrow on top end cell equals cell open parentheses table row 23 row 18 end table close parentheses end cell end table end style   

Jadi, diperoleh begin mathsize 14px style b with rightwards arrow on top plus 4 c with rightwards arrow on top plus a with rightwards arrow on top equals open parentheses table row 23 row 18 end table close parentheses end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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