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Jika u=2i+6j​−k dan v=i−j​+2k, tentukan vektor proyeksi ortogonal u terhadap v.

Pertanyaan

Jika u with rightwards arrow on top equals 2 i with hat on top plus 6 j with hat on top minus k with hat on top dan v with rightwards arrow on top equals i with hat on top minus j with hat on top plus 2 k with hat on top, tentukan vektor proyeksi ortogonal u with rightwards arrow on top terhadap v with rightwards arrow on top.

 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Pembahasan

Ingat kembali jika terdapat vektor a with rightwards arrow on top dan vektor b with rightwards arrow on top maka proyeksi orthogonal vektor a with rightwards arrow on toppada vektor b with rightwards arrow on top adalah 

proyeksi vektor = open parentheses fraction numerator a with rightwards arrow on top times b with rightwards harpoon with barb upwards on top over denominator open vertical bar b with rightwards arrow on top close vertical bar squared end fraction close parentheses times b with rightwards arrow on top

Jika  u with rightwards arrow on top equals 2 i with hat on top plus 6 j with hat on top minus k with hat on top dan v with rightwards arrow on top equals i with hat on top minus j with hat on top plus 2 k with hat on top maka proyeksi ortogonal u with rightwards arrow on top terhadap v with rightwards arrow on top adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator u with rightwards arrow on top times v with rightwards harpoon with barb upwards on top over denominator open vertical bar v with rightwards arrow on top close vertical bar squared end fraction close parentheses times v with rightwards arrow on top end cell equals cell open parentheses fraction numerator open parentheses table row 2 row 6 row cell negative 1 end cell end table close parentheses times open parentheses table row 1 row cell negative 1 end cell row 2 end table close parentheses over denominator 6 end fraction close parentheses times open parentheses table row 1 row cell negative 1 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses fraction numerator negative 6 over denominator 6 end fraction close parentheses open parentheses table row 1 row cell negative 1 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 1 row cell negative 2 end cell end table close parentheses end cell end table

Dengan demikian, vektor proyeksi ortogonal u with rightwards arrow on top terhadap v with rightwards arrow on top dalah open parentheses negative 1 comma space 1 comma space minus 2 close parentheses.

 

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