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Proyeksi skalar vektor  pada  adalah . Vektor  dan  dengan , maka nilai

Pertanyaan

Proyeksi skalar vektor a with rightwards arrow on top pada b with rightwards arrow on top adalah 6. Vektor a with rightwards arrow on top equals open parentheses table row x row cell negative 4 end cell row y end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 1 row 2 end table close parentheses dengan open vertical bar a with rightwards arrow on top close vertical bar equals square root of 89, maka nilai x equals space... 

  1. negative 6 

  2. negative 3 

  3. 3 

  4. 6 

  5. 8 

Pembahasan Soal:

Proyeksi skalar vektor a with rightwards arrow on top pada b with rightwards arrow on top adalah 6, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar c close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row 6 equals cell fraction numerator open parentheses table row x row cell negative 4 end cell row y end table close parentheses times open parentheses table row cell negative 2 end cell row 1 row 2 end table close parentheses over denominator square root of open parentheses negative 2 close parentheses squared plus open parentheses 1 close parentheses squared plus open parentheses 2 close parentheses squared end root end fraction end cell row 6 equals cell fraction numerator open parentheses negative 2 x close parentheses plus open parentheses negative 4 close parentheses plus open parentheses 2 y close parentheses over denominator square root of 9 end fraction end cell row 6 equals cell fraction numerator negative 2 x plus 2 y minus 4 over denominator 3 end fraction end cell row 18 equals cell negative 2 x plus 2 y minus 4 end cell row cell 2 x minus 2 y end cell equals 22 row cell x minus y end cell equals 11 row y equals cell x minus 11 space space... space open parentheses 1 close parentheses end cell end table   

open vertical bar a with rightwards arrow on top close vertical bar equals square root of 89, maka dengan mneggunakan rumus panjang vektor diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of x squared plus open parentheses negative 4 close parentheses squared plus y squared end root end cell equals cell square root of 89 end cell row cell x squared plus open parentheses negative 4 close parentheses squared plus y squared end cell equals 89 row cell x squared plus 16 plus y squared end cell equals 89 row cell x squared plus y squared end cell equals cell 89 minus 16 end cell row cell x squared plus y squared end cell equals cell 73 space... space open parentheses 2 close parentheses end cell end table 

Substitusi persamaan open parentheses 1 close parentheses ke persamaan open parentheses 2 close parentheses, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 73 row cell x squared plus open parentheses x minus 11 close parentheses squared end cell equals 73 row cell x squared plus x squared minus 22 x plus 121 end cell equals 73 row cell 2 x squared minus 22 x plus 48 end cell equals 0 row cell x squared minus 11 x plus 24 end cell equals 0 row cell open parentheses x minus 3 close parentheses open parentheses x minus 8 close parentheses end cell equals 0 row cell x minus 3 end cell equals cell 0 space space atau space space x minus 8 equals 0 end cell row x equals cell 3 space space atau space space space space space space space x equals 8 end cell end table 

Dengan demikian, jawaban yang tepata dalah C atau E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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