Roboguru

Bila ditentukan vektor  dan  maka proyeksi vektor orthogonal  pada  adalah ...

Pertanyaan

Bila ditentukan vektor q with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 6 end table close parentheses dan r with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row cell negative 3 end cell end table close parentheses maka proyeksi vektor orthogonal r with rightwards arrow on top pada q with rightwards arrow on top adalah ...

Pembahasan Soal:

Akan ditentukan proyeksi vektor orthogonal r with rightwards arrow on top pada q with rightwards arrow on top

equals open parentheses fraction numerator r with rightwards arrow on top times q with rightwards arrow on top over denominator open vertical bar q with rightwards arrow on top close vertical bar squared end fraction close parentheses q with rightwards arrow on top equals open parentheses fraction numerator left parenthesis negative 1 comma space minus 3 right parenthesis times left parenthesis negative 3 comma space 6 right parenthesis over denominator open parentheses square root of left parenthesis negative 3 right parenthesis squared plus 6 squared end root close parentheses squared end fraction close parentheses open parentheses negative 3 comma space 6 close parentheses equals open parentheses fraction numerator open parentheses negative 1 close parentheses cross times open parentheses negative 3 close parentheses plus open parentheses negative 3 close parentheses cross times 6 over denominator open parentheses square root of 9 plus 36 end root close parentheses squared end fraction close parentheses open parentheses negative 3 comma space 6 close parentheses equals open parentheses fraction numerator 3 plus left parenthesis negative 18 right parenthesis over denominator open parentheses square root of 45 close parentheses squared end fraction close parentheses open parentheses negative 3 comma space 6 close parentheses equals open parentheses fraction numerator 3 minus 18 over denominator 45 end fraction close parentheses open parentheses negative 3 comma space 6 close parentheses equals fraction numerator negative 15 over denominator 45 end fraction open parentheses negative 3 comma space 6 close parentheses equals negative 1 third open parentheses negative 3 comma space 6 close parentheses equals open parentheses 1 comma negative 2 close parentheses 

Jadi proyeksi vektor orthogonal r with rightwards arrow on top pada q with rightwards arrow on top adalah open parentheses 1 comma space minus 2 close parentheses.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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