Diketahui titik O titik pangkal, dan titik-titik A, B, dan C dengan vektor posisi OA=9i−10j​, OB=4i+2j​, dan OC=mi−2j​. a.  Tentukan vektor satuan yang searah AB

Pertanyaan

Diketahui titik begin mathsize 14px style O end style titik pangkal, dan titik-titik begin mathsize 14px style A comma space B comma space dan space C end style dengan vektor posisi begin mathsize 14px style stack O A with rightwards arrow on top equals 9 i with rightwards arrow on top minus 10 j with rightwards arrow on top comma space stack O B with rightwards arrow on top equals 4 i with rightwards arrow on top plus 2 j with rightwards arrow on top comma end style dan begin mathsize 14px style stack O C with rightwards arrow on top equals m i with rightwards arrow on top minus 2 j with rightwards arrow on top end style.

a.  Tentukan vektor satuan yang searah begin mathsize 14px style stack A B with rightwards arrow on top end style  

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Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

 vektor satuan yang searah begin mathsize 14px style stack A B with rightwards arrow on top end style adalah begin mathsize 14px style open parentheses table row cell negative 5 over 13 end cell row cell 12 over 13 end cell end table close parentheses end style.

Pembahasan

Vektor begin mathsize 14px style stack A B with rightwards arrow on top end style didapakan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top end cell row blank equals cell open parentheses table row 4 row 2 end table close parentheses minus open parentheses table row 9 row cell negative 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 end cell row 12 end table close parentheses end cell end table end style 

Vektor satuan yang searah begin mathsize 14px style stack A B with rightwards arrow on top end style didapatkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Vektor space satuan space stack A B with rightwards arrow on top end cell equals cell fraction numerator stack A B with rightwards arrow on top over denominator open vertical bar stack A B with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 5 end cell row 12 end table close parentheses over denominator square root of open parentheses negative 5 close parentheses squared plus 12 squared end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 5 end cell row 12 end table close parentheses over denominator square root of 25 plus 144 end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 5 end cell row 12 end table close parentheses over denominator square root of 169 end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 5 end cell row 12 end table close parentheses over denominator 13 end fraction end cell row blank equals cell open parentheses table row cell negative 5 over 13 end cell row cell 12 over 13 end cell end table close parentheses end cell end table end style 

Dengan demikian, vektor satuan yang searah begin mathsize 14px style stack A B with rightwards arrow on top end style adalah begin mathsize 14px style open parentheses table row cell negative 5 over 13 end cell row cell 12 over 13 end cell end table close parentheses end style.

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