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Pertanyaan

Diketahui: begin mathsize 14px style straight p with rightwards harpoon with barb upwards on top equals 2 straight i plus aj end style dan Error converting from MathML to accessible text.. Jika begin mathsize 14px style left parenthesis straight p with rightwards harpoon with barb upwards on top plus straight q with rightwards harpoon with barb upwards on top right parenthesis times left parenthesis straight p with rightwards harpoon with barb upwards on top minus straight q with rightwards harpoon with barb upwards on top right parenthesis equals negative 27 end style. Tentukan nilai begin mathsize 14px style a end style.

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style a end style yang memenuhi adalah begin mathsize 14px style straight a equals plus-or-minus square root of 10. end style 

Pembahasan

Diketahui :

 begin mathsize 14px style straight p with rightwards harpoon with barb upwards on top equals 2 straight i plus aj end style dan Error converting from MathML to accessible text..

Ditanya:

Jika begin mathsize 14px style left parenthesis straight p with rightwards harpoon with barb upwards on top plus straight q with rightwards harpoon with barb upwards on top right parenthesis times left parenthesis straight p with rightwards harpoon with barb upwards on top minus straight q with rightwards harpoon with barb upwards on top right parenthesis equals negative 27 end style. Tentukan nilai begin mathsize 14px style a end style.

Penyelesaian:

Untuk memudahkan kita ubah vektor menjadi bentuk kotak sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight p with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 2 row straight a end table close parentheses end cell row cell straight q with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 4 row cell negative 5 end cell end table close parentheses end cell row cell straight p with rightwards harpoon with barb upwards on top plus straight q with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 2 row straight a end table close parentheses plus open parentheses table row 4 row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row cell straight a minus 5 end cell end table close parentheses end cell row cell straight p with rightwards harpoon with barb upwards on top minus straight q with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 2 row straight a end table close parentheses minus open parentheses table row 4 row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row cell straight a plus 5 end cell end table close parentheses end cell end table end style  

Dengan konsep dot product maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight p with rightwards harpoon with barb upwards on top plus straight q with rightwards harpoon with barb upwards on top right parenthesis times left parenthesis straight p with rightwards harpoon with barb upwards on top minus straight q with rightwards harpoon with barb upwards on top right parenthesis end cell equals cell negative 27 end cell row cell open parentheses table row 6 row cell straight a minus 5 end cell end table close parentheses times open parentheses table row cell negative 2 end cell row cell straight a plus 5 end cell end table close parentheses end cell equals cell negative 27 end cell row cell left parenthesis 6 right parenthesis times left parenthesis negative 2 right parenthesis plus left parenthesis straight a minus 5 right parenthesis left parenthesis straight a plus 5 right parenthesis end cell equals cell negative 27 end cell row cell negative 12 plus straight a squared minus 25 end cell equals cell negative 27 end cell row cell straight a blank squared minus 37 end cell equals cell negative 27 end cell row cell straight a squared end cell equals 10 row straight a equals cell plus-or-minus square root of 10 end cell end table end style 

Jadi, nilai begin mathsize 14px style a end style yang memenuhi adalah begin mathsize 14px style straight a equals plus-or-minus square root of 10. end style 

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