Diketahui koordinat titik P(-4,2) dan Q(-1,6). Vektor satuan yang searah dengan vektor PQ⇀​ adalah...

Pertanyaan

Diketahui koordinat titik P(-4,2) dan Q(-1,6). Vektor satuan yang searah dengan vektor begin mathsize 14px style stack P Q with rightwards harpoon with barb upwards on top end style adalah...

M. Ardini

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

vektor satuannya adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank i end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 over 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank j end table end style 

Pembahasan

Diketahui:
begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P with rightwards harpoon with barb upwards on top end cell equals cell left parenthesis negative 4 comma 2 right parenthesis end cell row cell Q with rightwards arrow on top end cell equals cell left parenthesis negative 1 comma 6 right parenthesis end cell end table end style 

Ditanya:
begin mathsize 14px style stack P Q with hat on top end style 

Jawab

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack P Q with rightwards arrow on top end cell equals cell Q with rightwards arrow on top minus P with rightwards arrow on top end cell row blank equals cell left parenthesis 1 plus 4 right parenthesis comma left parenthesis 6 minus 2 right parenthesis end cell row blank equals cell left parenthesis 3 comma 4 right parenthesis end cell row blank equals cell 3 i plus 4 j end cell row blank blank blank row cell stack P Q with hat on top end cell equals cell fraction numerator stack P Q with rightwards arrow on top over denominator open vertical bar stack P Q with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 3 i plus 4 j over denominator square root of 3 squared plus 4 squared end root end fraction end cell row blank equals cell fraction numerator 3 i plus 4 j over denominator 5 end fraction end cell row blank equals cell 3 over 5 i plus 4 over 5 j end cell end table end style 

Jadi, vektor satuannya adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank i end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 over 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank j end table end style 

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