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Diketahui vektor a=⎝⎛​−217​⎠⎞​ dan b=⎝⎛​2−12​⎠⎞​. Tentukan proyeksi skalar orthogonal vektor b pada vektor a.

Pertanyaan

Diketahui vektor a with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 1 row 7 end table close parentheses dan b with rightwards arrow on top equals open parentheses table row 2 row cell negative 1 end cell row 2 end table close parentheses.

Tentukan proyeksi skalar orthogonal vektor b with rightwards arrow on top pada vektor a with rightwards arrow on top.

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Peroyeski skalar ortogonal vektor b with rightwards arrow on top pada vektor a with rightwards arrow on top dapat menggunkan rumus:

equals fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction

Sehingga:

equals fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction equals fraction numerator open parentheses negative 2 comma 1 comma 7 close parentheses times open parentheses 2 comma negative 1 comma 2 close parentheses over denominator square root of open parentheses negative 2 close parentheses squared plus open parentheses 1 close parentheses squared plus open parentheses 7 close parentheses squared end root end fraction equals fraction numerator negative 4 plus open parentheses negative 1 close parentheses plus 14 over denominator square root of 4 plus 1 plus 49 end root end fraction equals fraction numerator 9 over denominator square root of 54 end fraction equals fraction numerator 9 over denominator 3 square root of 6 end fraction equals fraction numerator 3 over denominator square root of 6 end fraction equals fraction numerator square root of 6 over denominator 2 end fraction

Peroyeski skalar ortogonal vektor b with rightwards arrow on top pada vektor a with rightwards arrow on topadalah fraction numerator square root of 6 over denominator 2 end fraction 

152

5.0 (4 rating)

Pertanyaan serupa

1. Jika a=⎝⎛​231​⎠⎞​, b=⎝⎛​5−2−4​⎠⎞​, dan c=⎝⎛​10−1319​⎠⎞​, buktikan bahwa ketiga vektor tersebut saling tegak lurus.

206

3.0

Jawaban terverifikasi

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