Roboguru

Diketahui  dan . Tentukan besar sudut antara vektor  dan .

Pertanyaan

Diketahui open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar equals square root of 2 comma space open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar equals square root of 9 comma dan open vertical bar a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top close vertical bar equals square root of 5. Tentukan besar sudut antara vektor a with rightwards harpoon with barb upwards on top dan b with rightwards harpoon with barb upwards on top.

Pembahasan Soal:

Karena yang diketahui adalah panjang vektor a with rightwards harpoon with barb upwards on top, panjang vektor b with rightwards harpoon with barb upwards on top, dan panjang jumlah kedua vektor, kita dapat menggunakan persamaan

 open vertical bar a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top close vertical bar equals square root of open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar squared plus open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar squared plus 2 open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar times cos space theta end root 

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards harpoon with barb upwards on top plus b with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 5 end cell row cell square root of open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar squared plus open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar squared plus 2 open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar times cos space theta end root end cell equals cell square root of 5 end cell row cell open parentheses square root of open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar squared plus open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar squared plus 2 open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar times cos space theta end root close parentheses squared end cell equals cell open parentheses square root of 5 close parentheses squared end cell row cell open parentheses square root of 2 close parentheses squared plus open parentheses square root of 9 close parentheses squared plus 2 times square root of 2 times square root of 9 times cos space theta end cell equals 5 row cell 2 plus 9 plus 2 times square root of 2 times 3 times cos space theta end cell equals 5 row cell 11 plus 6 square root of 2 times c os space theta end cell equals 5 row cell 6 square root of 2 times cos space theta end cell equals cell 5 minus 11 end cell row cell cos space theta end cell equals cell fraction numerator negative 6 over denominator 6 square root of 2 end fraction end cell row cell cos space theta end cell equals cell negative fraction numerator 1 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row cell cos space theta end cell equals cell negative 1 half square root of 2 end cell row cell space theta end cell equals cell arccos open parentheses negative 1 half square root of 2 close parentheses end cell row cell space straight theta end cell equals cell 135 degree end cell end table end style     

Jadi, besar sudut antara vektor a with rightwards harpoon with barb upwards on top dan b with rightwards harpoon with barb upwards on top adalah 135 degree.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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