Nilai kosinus sudut antara vektor u=(3−6​) dan v=(4−3​) adalah... .

Pertanyaan

Nilai kosinus sudut antara vektor u with rightwards arrow on top equals open parentheses table row 3 row cell negative 6 end cell end table close parentheses dan v with rightwards arrow on top equals open parentheses table row 4 row cell negative 3 end cell end table close parentheses adalah... .

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui vektor u with rightwards arrow on top equals open parentheses table row 3 row cell negative 6 end cell end table close parentheses dan v with rightwards arrow on top equals open parentheses table row 4 row cell negative 3 end cell end table close parentheses. Misal theta adalah sudut diantara dua vektor tersebut maka nilai kosinus sudut tersebut sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator u with rightwards arrow on top times v with rightwards arrow on top over denominator open vertical bar u with rightwards arrow on top close vertical bar open vertical bar v with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row 3 row cell negative 6 end cell end table close parentheses times open parentheses table row 4 row cell negative 3 end cell end table close parentheses over denominator open square brackets square root of 3 squared plus open parentheses negative 6 close parentheses squared end root close square brackets space open square brackets square root of 4 squared plus open parentheses negative 3 close parentheses squared end root close square brackets end fraction end cell row blank equals cell fraction numerator 12 plus 18 over denominator open parentheses square root of 9 plus 36 end root close parentheses open parentheses square root of 16 plus 9 end root close parentheses end fraction end cell row blank equals cell fraction numerator 30 over denominator open parentheses square root of 45 close parentheses open parentheses square root of 25 close parentheses end fraction end cell row blank equals cell fraction numerator 30 over denominator open parentheses square root of 9 times 5 end root close parentheses times 5 end fraction end cell row blank equals cell fraction numerator 30 over denominator 3 times 5 square root of 5 end fraction end cell row blank equals cell fraction numerator 30 over denominator 15 square root of 5 end fraction times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 2 square root of 5 over denominator 5 end fraction end cell row blank equals cell 2 over 5 square root of 5 end cell end table 
 

Jadi, nilai kosinus sudut antara vektor u with rightwards arrow on top equals open parentheses table row 3 row cell negative 6 end cell end table close parentheses dan v with rightwards arrow on top equals open parentheses table row 4 row cell negative 3 end cell end table close parentheses adalah 2 over 5 square root of 5.

 

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Diketahui dua vektor yang mempunyai besar yang sama, yaitu 10 satuan. Jika resultannya 10, kedua vektor tersebut membentuk sudut ....

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