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Pertanyaan

Diketahui vektor u with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row cell negative 2 end cell row 4 end table close parentheses dan v with rightwards arrow on top equals open parentheses table row 2 row cell negative 4 end cell row 3 end table close parentheses. Tentukan proyeksi vektor ortogonal left parenthesis u with rightwards arrow on top plus 2 v with rightwards arrow on top right parenthesis pada open parentheses 2 u with rightwards arrow on top minus v with rightwards arrow on top close parentheses.

 

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Menentukan left parenthesis u with rightwards arrow on top plus 2 v with rightwards arrow on top right parenthesis

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis u with rightwards arrow on top plus 2 v with rightwards arrow on top right parenthesis end cell equals cell open parentheses table row cell negative 1 end cell row cell negative 2 end cell row 4 end table close parentheses plus 2 open parentheses table row 2 row cell negative 4 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row cell negative 2 end cell row 4 end table close parentheses plus open parentheses table row 4 row cell negative 8 end cell row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 plus 4 end cell row cell negative 2 plus left parenthesis negative 8 right parenthesis end cell row cell 4 plus 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative 10 end cell row 10 end table close parentheses end cell end table 

Menentukan open parentheses 2 u with rightwards arrow on top minus v with rightwards arrow on top close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 u with rightwards arrow on top minus v with rightwards arrow on top close parentheses end cell row blank equals cell 2 open parentheses table row cell negative 1 end cell row cell negative 2 end cell row 4 end table close parentheses minus open parentheses table row 2 row cell negative 4 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row cell negative 4 end cell row 8 end table close parentheses minus open parentheses table row 2 row cell negative 4 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 minus 2 end cell row cell negative 4 plus 4 end cell row cell 8 minus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 0 row 5 end table close parentheses end cell end table 

Menentukan proyeksi vektor ortogonal left parenthesis u with rightwards arrow on top plus 2 v with rightwards arrow on top right parenthesis pada open parentheses 2 u with rightwards arrow on top minus v with rightwards arrow on top close parentheses.

equals left parenthesis fraction numerator left parenthesis u with rightwards arrow on top plus 2 v with rightwards arrow on top right parenthesis times left parenthesis 2 u with rightwards arrow on top minus v with rightwards arrow on top right parenthesis over denominator vertical line left parenthesis 2 u with rightwards arrow on top minus v with rightwards arrow on top right parenthesis vertical line squared end fraction right parenthesis left parenthesis 2 u with rightwards arrow on top minus v with rightwards arrow on top right parenthesis equals fraction numerator left parenthesis 3 cross times left parenthesis negative 4 right parenthesis plus left parenthesis left parenthesis negative 10 right parenthesis cross times 0 right parenthesis plus left parenthesis 10 cross times 5 right parenthesis over denominator left parenthesis square root of left parenthesis negative 4 right parenthesis squared plus 0 squared plus 5 squared end root right parenthesis squared end fraction open parentheses table row cell negative 4 end cell row 0 row 5 end table close parentheses equals fraction numerator negative 12 plus 0 plus 50 over denominator left parenthesis square root of 16 plus 25 end root right parenthesis squared end fraction open parentheses table row cell negative 4 end cell row 0 row 5 end table close parentheses equals 38 over left parenthesis square root of 41 right parenthesis squared open parentheses table row cell negative 4 end cell row 0 row 5 end table close parentheses equals 38 over 41 open parentheses table row cell negative 4 end cell row 0 row 5 end table close parentheses equals open parentheses table row cell fraction numerator negative 152 over denominator 41 end fraction end cell row 0 row cell 190 over 41 end cell end table close parentheses 

Jadi, proyeksi vektor ortogonalnya adalah open parentheses table row cell fraction numerator negative 152 over denominator 41 end fraction end cell row 0 row cell 190 over 41 end cell end table close parentheses .

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