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Pertanyaan

Jika a with rightwards arrow on top equals 5 i minus 5 jb with rightwards arrow on top equals 4 i minus 5 j, dan c with rightwards arrow on top equals 4 i plus 5 j. Tentukan vektor a with rightwards arrow on top plus open parentheses b with rightwards arrow on top minus 2 c with rightwards arrow on top close parentheses!

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses b with rightwards arrow on top minus 2 c with rightwards arrow on top close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank i end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 20 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank j end table.

Pembahasan

Misalkan table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell x subscript 1 space i plus y subscript 1 space j space dan space b with rightwards arrow on top equals x subscript 2 space i plus y subscript 2 space j end cell end table maka dapat ditentukan:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus b with rightwards arrow on top end cell equals cell open parentheses x subscript 1 plus x subscript 2 close parentheses space i plus open parentheses y subscript 1 plus y subscript 2 close parentheses space j end cell row cell a with rightwards arrow on top minus b with rightwards arrow on top end cell equals cell open parentheses x subscript 1 minus x subscript 2 close parentheses space i plus open parentheses y subscript 1 minus y subscript 2 close parentheses space j end cell row cell 2 a with rightwards arrow on top end cell equals cell 2 x subscript 1 space i plus 2 y subscript 1 space j end cell end table 

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell 5 i minus 5 j end cell row cell b with rightwards arrow on top end cell equals cell 4 i minus 5 j end cell row cell c with rightwards arrow on top end cell equals cell 4 i plus 5 j end cell end table 

Sehingga dapat ditentukan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 c with rightwards arrow on top end cell equals cell 2 open parentheses 4 i plus 5 j close parentheses end cell row blank equals cell 8 i plus 10 j end cell row cell open parentheses b with rightwards arrow on top minus 2 c with rightwards arrow on top close parentheses end cell equals cell open parentheses 4 i minus 5 j close parentheses minus open parentheses 8 i plus 10 j close parentheses end cell row blank equals cell open parentheses 4 minus 8 close parentheses i plus open parentheses negative 5 minus 10 close parentheses j end cell row blank equals cell negative 4 i minus 15 j end cell row cell a with rightwards arrow on top plus open parentheses b with rightwards arrow on top minus 2 c with rightwards arrow on top close parentheses end cell equals cell open parentheses 5 i minus 5 j close parentheses plus open parentheses negative 4 i minus 15 j close parentheses end cell row blank equals cell open parentheses 5 minus 4 close parentheses i plus open parentheses negative 5 minus 15 close parentheses j end cell row blank equals cell i minus 20 j end cell end table 

Dengan demikian, diperoleh table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses b with rightwards arrow on top minus 2 c with rightwards arrow on top close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank i end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 20 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank j end table.

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