Diketahui vektor a=6i−2j​+3k dan b=4i+4j​−2k. tentukan: d. proyeksi vektor ortogonal dari vektor b pada arah vektor a

Pertanyaan

Diketahui vektor a with rightwards arrow on top equals 6 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus 3 k with rightwards arrow on top dan b with rightwards arrow on top equals 4 i with rightwards arrow on top plus 4 j with rightwards arrow on top minus 2 k with rightwards arrow on top. tentukan:

d. proyeksi vektor ortogonal dari vektor b with rightwards arrow on top pada arah vektor a with rightwards arrow on top

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 60 over 49 i with rightwards arrow on top minus 20 over 49 j with rightwards arrow on top plus 30 over 49 k with rightwards arrow on top end cell end table

Ingat!

Proyeksi vektor ortogonal a with rightwards arrow on top pada vektor b with rightwards arrow on top adalah sebagai berikut

c with rightwards arrow on top equals open parentheses 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 squared end fraction close parentheses times a with rightwards arrow on top  

maka,proyeksi vektor ortogonal dari vektor b with rightwards arrow on top pada arah vektor a with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell c with rightwards arrow on top end cell equals cell open parentheses 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 squared end fraction close parentheses times a with rightwards arrow on top end cell row blank equals cell open parentheses fraction numerator 6 times 4 plus open parentheses negative 2 close parentheses open parentheses 4 close parentheses plus open parentheses 3 close parentheses open parentheses negative 2 close parentheses over denominator open parentheses square root of 6 squared plus open parentheses negative 2 close parentheses squared plus open parentheses 3 close parentheses squared end root close parentheses squared end fraction close parentheses open parentheses 6 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus 3 k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses fraction numerator 24 minus 8 minus 6 over denominator open parentheses square root of 36 plus 4 plus 9 end root close parentheses squared end fraction close parentheses open parentheses 6 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus 3 k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 10 over 49 close parentheses open parentheses 6 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus 3 k with rightwards arrow on top close parentheses end cell row blank equals cell 60 over 49 i with rightwards arrow on top minus 20 over 49 j with rightwards arrow on top plus 30 over 49 k with rightwards arrow on top end cell end table 

dengan demikian, proyeksi vektor ortogonal dari vektor a with rightwards arrow on top pada arah vektor b with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 60 over 49 i with rightwards arrow on top minus 20 over 49 j with rightwards arrow on top plus 30 over 49 k with rightwards arrow on top end cell end table

87

4.0 (2 rating)

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