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Diketahui panjang vektor a=−6, panjang vektor b=4 dan besar sudut antara vektor a dan b adalah 90∘. Tentukan panjang vektor ∣∣​a−b∣∣​

Pertanyaan

Diketahui panjang vektor a with rightwards arrow on top equals negative 6, panjang vektor b with rightwards arrow on top equals 4 dan besar sudut antara vektor a with rightwards arrow on top dan b with rightwards arrow on top adalah begin mathsize 14px style 90 degree end style. Tentukan panjang vektor open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

panjang vektor open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar adalah 2 square root of 13 

Pembahasan

Diketahui :

open vertical bar a with rightwards arrow on top close vertical bar equals negative 6 open vertical bar b with rightwards arrow on top close vertical bar equals 4 theta equals 90 degree 

Ditanya : open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar

Jawab :

Dengan menggunakan rumus mencari panjang selisih dua vektor maka diperoleh perhitungan seperti berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell open vertical bar a with rightwards harpoon with barb upwards on top minus b with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of open vertical bar a close vertical bar squared plus open vertical bar b close vertical bar squared minus 2 times open vertical bar a close vertical bar times open vertical bar b close vertical bar times cos space theta end root end cell row blank equals cell square root of open parentheses negative 6 close parentheses squared plus open parentheses 4 close parentheses squared minus 2 times open parentheses negative 6 close parentheses times open parentheses 4 close parentheses times cos space 90 degree end root end cell row blank equals cell square root of 36 plus 16 minus open parentheses left parenthesis negative 48 right parenthesis times 0 close parentheses end root end cell row blank equals cell square root of 52 end cell row blank equals cell 2 square root of 13 end cell end table 

Jadi, panjang vektor open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar adalah 2 square root of 13 

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Tentukan besar selisihS=p​−q​dari vektor-vektor berikut. c. p​=(16−2​) dan q​=(4−3​)

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Jawaban terverifikasi

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