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Diketahui vektor , , dan . Tentukan d.

Diketahui vektor begin mathsize 14px style a with rightwards arrow on top equals 2 i with hat on top plus 3 j with hat on top end stylebegin mathsize 14px style b with rightwards arrow on top equals i with hat on top minus 4 j with hat on top end style, dan begin mathsize 14px style c with rightwards arrow on top equals 4 j with hat on top end style. Tentukan

d. begin mathsize 14px style 1 half c with rightwards arrow on top minus a with rightwards arrow on top end style 

  1. ...space 

  2. ...space 

Jawaban:

Ingat rumus perkalian skalar dengan vektor dan rumus pengurangan vektor adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell k a with rightwards arrow on top end cell equals cell k open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses equals open parentheses table row cell k a subscript 1 end cell row cell k a subscript 2 end cell end table close parentheses end cell row cell a with rightwards arrow on top minus b with rightwards arrow on top end cell equals cell open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses minus open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses equals open parentheses table row cell a subscript 1 minus b subscript 1 end cell row cell a subscript 2 minus b subscript 2 end cell end table close parentheses end cell end table end style  

Dari soal di atas, diketahui begin mathsize 14px style c with rightwards arrow on top end style dan begin mathsize 14px style a with rightwards arrow on top end style sebagai berikut.

begin mathsize 14px style c with rightwards arrow on top equals 4 j with hat on top equals open parentheses table row 0 row 4 end table close parentheses a with rightwards arrow on top equals 2 i with hat on top plus 3 j with hat on top equals open parentheses table row 2 row 3 end table close parentheses end style 

Dengan menggunakan rumus perkalian skalar dengan vektor dan rumus pengurangan vektor di atas, maka diperoleh perhitungan sebagai berikut. 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 1 half c with rightwards arrow on top minus a with rightwards arrow on top end cell equals cell 1 half open parentheses table row 0 row 4 end table close parentheses minus open parentheses table row 2 row 3 end table close parentheses end cell row blank equals cell open parentheses table row 0 row 2 end table close parentheses minus open parentheses table row 2 row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell negative 2 i with hat on top minus j with hat on top end cell end table end style 

Dengan demikian nilai dari begin mathsize 14px style 1 half c with rightwards arrow on top minus a with rightwards arrow on top end style adalah begin mathsize 14px style negative 2 i with hat on top minus j with hat on top end style.

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