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Pertanyaan

Diketahui vektor straight a with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row cell negative 2 end cell row 2 end table close parentheses dan straight b with rightwards arrow on top equals open parentheses table row 5 row cell negative 1 end cell row 4 end table close parentheses. Proyeksi orthogonal vektor straight a with rightwards arrow on top pada vektor straight b with rightwards arrow on top adalah ...

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

proyeksi orthogonal vektor straight a with rightwards arrow on top pada vektor straight b with rightwards arrow on top adalah adalah straight c with rightwards arrow on top equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 25 over 21 end cell row cell 5 over 21 end cell row cell negative 20 over 21 end cell end table close parentheses end cell end table.

Pembahasan

Ingat konsep perkalian titik dari dua vektor dan panjang vektor, maka proyeksi orthogonal vektor straight a with rightwards arrow on top pada vektor straight b with rightwards arrow on top adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight c with rightwards arrow on top end cell equals cell fraction numerator straight a with rightwards arrow on top times straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar squared end fraction times straight b with rightwards arrow on top end cell row blank equals cell fraction numerator open parentheses table row cell negative 4 end cell row cell negative 2 end cell row 2 end table close parentheses times open parentheses table row 5 row cell negative 1 end cell row 4 end table close parentheses over denominator open parentheses square root of 5 squared plus open parentheses negative 1 close parentheses squared plus open parentheses 4 close parentheses squared end root close parentheses squared end fraction times open parentheses table row 5 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell fraction numerator open parentheses negative 4 cross times 5 close parentheses plus open parentheses negative 2 cross times negative 1 close parentheses plus open parentheses 2 cross times 4 close parentheses over denominator open parentheses square root of 25 plus 1 plus 16 end root close parentheses squared end fraction times open parentheses table row 5 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell fraction numerator negative 20 plus 2 plus 8 over denominator open parentheses square root of 42 close parentheses squared end fraction times open parentheses table row 5 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell fraction numerator negative 10 over denominator 42 end fraction times open parentheses table row 5 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell negative 5 over 21 times open parentheses table row 5 row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 25 over 21 end cell row cell 5 over 21 end cell row cell negative 20 over 21 end cell end table close parentheses end cell end table 

Dengan demikian proyeksi orthogonal vektor straight a with rightwards arrow on top pada vektor straight b with rightwards arrow on top adalah adalah straight c with rightwards arrow on top equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 25 over 21 end cell row cell 5 over 21 end cell row cell negative 20 over 21 end cell end table close parentheses end cell end table.

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