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Diketahui koordinat , , dan . Tentukan panjang vektor !

Pertanyaan

Diketahui koordinat begin mathsize 14px style text A  end text open parentheses 3 comma space 2 close parentheses end stylebegin mathsize 14px style text B  end text open parentheses negative 4 comma space 1 close parentheses end style, dan begin mathsize 14px style text C end text open parentheses negative 1 comma space 5 close parentheses end style. Tentukan panjang vektor begin mathsize 14px style A B plus B C plus A C end style!

Pembahasan Soal:

Menentukan vektor begin mathsize 14px style A B comma space B C comma space text dan end text space A C end style sebagai berikut.

begin mathsize 14px style 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 table row cell negative 4 end cell row 1 end table close parentheses minus open parentheses table row 3 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 7 end cell row cell negative 1 end cell end table close parentheses end cell end table end style

begin mathsize 14px style 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 table row cell negative 1 end cell row 5 end table close parentheses minus open parentheses table row cell negative 4 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 4 end table close parentheses end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A C end cell equals cell C minus A end cell row blank equals cell open parentheses table row cell negative 1 end cell row 5 end table close parentheses minus open parentheses table row 3 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 3 end table close parentheses end cell end table end style

Diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A B plus B C plus A C end cell equals cell open parentheses table row cell negative 7 end cell row cell negative 1 end cell end table close parentheses plus open parentheses table row 3 row 4 end table close parentheses plus open parentheses table row cell negative 4 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 8 end cell row 6 end table close parentheses end cell end table end style

Panjang vektor begin mathsize 14px style A B plus B C plus A C end style, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar A B plus B C plus A C close vertical bar end cell equals cell square root of open parentheses negative 8 close parentheses squared plus 6 squared end root end cell row blank equals cell square root of 64 plus 36 end root end cell row blank equals cell square root of 100 end cell row blank equals 10 end table end style

Dengan demikian, panjang vektor begin mathsize 14px style A B plus B C plus A C end style adalah 10.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Maret 2021

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