Pertanyaan

Besar sudut antara vektor u ⇀ = ⎝ ⎛ 4 − 5 2 ⎠ ⎞ dan v ⇀ = ⎝ ⎛ 3 2 − 1 ⎠ ⎞ adalah ...

Besar sudut antara vektor $u ⇀ = ⎝ ⎛ 4 - 5 2 ⎠ ⎞$ dan $v ⇀ = ⎝ ⎛ 32 - 1 ⎠ ⎞$ adalah ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Rumus besar sudut antara dua vektor yaitu: Sehingga dipeorleh: Maka, besar sudut antara vektor dan adalah .

Rumus besar sudut antara dua vektor yaitu:

$cos space alpha equals fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator open vertical bar u with rightwards harpoon with barb upwards on top close vertical bar open vertical bar v with rightwards harpoon with barb upwards on top close vertical bar end fraction$

Sehingga dipeorleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator u with rightwards harpoon with barb upwards on top times v with rightwards harpoon with barb upwards on top over denominator open vertical bar u with rightwards harpoon with barb upwards on top close vertical bar open vertical bar v with rightwards harpoon with barb upwards on top close vertical bar end fraction end cell row cell cos space alpha end cell equals cell fraction numerator open parentheses 4 cross times 3 close parentheses plus open parentheses negative 5 cross times 2 close parentheses plus open parentheses 2 cross times open parentheses negative 1 close parentheses close parentheses over denominator square root of 4 squared plus open parentheses negative 5 close parentheses squared plus 2 squared end root times square root of 3 squared plus 2 squared plus open parentheses negative 1 close parentheses squared end root end fraction end cell row cell cos space alpha end cell equals cell fraction numerator 12 plus open parentheses negative 10 close parentheses plus open parentheses negative 2 close parentheses over denominator square root of 16 plus 25 plus 4 end root times square root of 9 plus 4 plus 1 end root end fraction end cell row cell cos space alpha end cell equals cell fraction numerator 12 minus 10 minus 2 over denominator square root of 45 times square root of 14 end fraction end cell row cell cos space alpha end cell equals cell fraction numerator 0 over denominator square root of 630 end fraction end cell row cell cos space alpha end cell equals 0 row alpha equals cell arc space cos space 0 end cell row alpha equals cell 90 degree end cell end table$

Maka, besar sudut antara vektor u with rightwards harpoon with barb upwards on top equals open parentheses table row 4 row cell negative 5 end cell row 2 end table close parentheses dan v with rightwards harpoon with barb upwards on top equals open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses adalah 90 degree .

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