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Diketahui 3 titik ,,  dan . Tentukan panjang proye...

Diketahui 3 titik A left parenthesis 4 comma negative 1 comma 2 right parenthesis,space B left parenthesis 4 comma 3 comma negative 2 right parenthesis,  dan C left parenthesis 1 comma 3 comma 2 right parenthesis. Tentukan panjang proyeksi vektor AB poda BC

Jawaban:

Pertama kita tentukan vektor AB dan BC:

table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals cell B minus A end cell row blank equals cell open parentheses 4 comma 3 comma negative 2 close parentheses minus open parentheses 4 comma negative 1 comma 2 close parentheses end cell row blank equals cell open parentheses 0 comma 4 comma negative 4 close parentheses end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell B C end cell equals cell C minus B end cell row blank equals cell open parentheses 1 comma 3 comma 2 close parentheses minus open parentheses 4 comma 3 comma negative 2 close parentheses end cell row blank equals cell open parentheses negative 3 comma 0 comma 4 close parentheses end cell end table

Sehingga, Untuk mentukan panjang proyeksi vektor AB poda BC dapat menggunakan rumus:

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell fraction numerator A B times B C over denominator open vertical bar B C close vertical bar end fraction end cell row blank equals cell fraction numerator open square brackets table row cell negative 1 end cell row 5 row 1 end table close square brackets times open square brackets table row 3 row 0 row 4 end table close square brackets over denominator square root of open parentheses negative 3 close parentheses squared plus open parentheses 0 close parentheses squared plus open parentheses 4 close parentheses squared end root end fraction end cell row blank equals cell fraction numerator negative 3 plus 0 plus 4 over denominator square root of 9 plus 16 end root end fraction end cell row blank equals cell 1 fifth end cell row blank equals cell 7 over blank end cell end table

Jadi, panjang proyeksi vektor AB poda BC adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fifth end cell end table

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