Roboguru

Diberikan tiga buah vektor , , dan . Jika . Tentuk...

Diberikan tiga buah vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals straight i with rightwards harpoon with barb upwards on top plus 2 straight j with rightwards harpoon with barb upwards on top end stylebegin mathsize 14px style straight b with rightwards harpoon with barb upwards on top equals negative 4 straight i with rightwards harpoon with barb upwards on top minus 3 straight j with rightwards harpoon with barb upwards on top end style, dan begin mathsize 14px style straight c with rightwards harpoon with barb upwards on top equals 5 straight i with rightwards harpoon with barb upwards on top minus 2 straight j with rightwards harpoon with barb upwards on top end style. Jika begin mathsize 14px style straight w with rightwards harpoon with barb upwards on top equals straight a with rightwards harpoon with barb upwards on top minus 2 straight b with rightwards harpoon with barb upwards on top plus 3 straight c with rightwards harpoon with barb upwards on top end style. Tentukan begin mathsize 14px style open vertical bar straight w with rightwards harpoon with barb upwards on top close vertical bar equals... end style?

Jawaban:

Perhatikan perhitungan berikut.

Ingat, panjang vektor:

begin mathsize 14px style open vertical bar straight a with rightwards harpoon with barb upwards on top close vertical bar equals square root of x squared plus y squared end root end style

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight w with rightwards harpoon with barb upwards on top end cell equals cell straight a with rightwards harpoon with barb upwards on top minus 2 straight b with rightwards harpoon with barb upwards on top plus 3 straight c with rightwards harpoon with barb upwards on top end cell row blank equals cell straight i with rightwards harpoon with barb upwards on top plus 2 straight j with rightwards harpoon with barb upwards on top minus 2 open parentheses negative 4 straight i with rightwards harpoon with barb upwards on top minus 3 straight j with rightwards harpoon with barb upwards on top close parentheses plus 3 open parentheses 5 straight i with rightwards harpoon with barb upwards on top minus 2 straight j with rightwards harpoon with barb upwards on top close parentheses end cell row blank equals cell straight i with rightwards harpoon with barb upwards on top plus 2 straight j with rightwards harpoon with barb upwards on top plus 8 straight i with rightwards harpoon with barb upwards on top plus 6 straight j with rightwards harpoon with barb upwards on top plus 15 straight i with rightwards harpoon with barb upwards on top minus 6 straight j with rightwards harpoon with barb upwards on top end cell row blank equals cell 24 straight i with rightwards harpoon with barb upwards on top plus 2 straight j with rightwards harpoon with barb upwards on top end cell end table end style

sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight w with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 24 squared plus 2 squared end root end cell row blank equals cell square root of 576 plus 4 end root end cell row blank equals cell square root of 580 end cell row blank blank blank end table end style

Jadi, begin mathsize 14px style open vertical bar straight w with rightwards harpoon with barb upwards on top close vertical bar end style adalah begin mathsize 14px style square root of 580 end style.

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