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Diketahui bold italic a equals 3 bold italic i with bold hat on top minus 4 bold italic j with bold hat on top plus 2 bold italic k with bold hat on top dan titik straight P open parentheses 2 comma space minus 1 comma space 3 close parentheses. Jika panjang PQ with rightwards harpoon with barb upwards on top sama dengan panjang bold italic a dan PQ with rightwards harpoon with barb upwards on top berlawanan arah dengan bold italic a, tentukan koordinat straight Q.space 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Misalkan koordinat straight Q adalah open parentheses k comma space l comma space m close parentheses dan diketahui straight P open parentheses 2 comma space minus 1 comma space 3 close parentheses. Berarti vektor posisi dari masing-masing titik adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell stack O Q with rightwards harpoon with barb upwards on top end cell equals cell open parentheses k comma space l comma space m close parentheses end cell row cell stack O P with rightwards harpoon with barb upwards on top end cell equals cell open parentheses 2 comma space minus 1 comma space 3 close parentheses end cell end table 

 Maka dapat diperoleh vektor stack P Q with rightwards harpoon with barb upwards on top sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell stack P Q with rightwards harpoon with barb upwards on top end cell equals cell stack O Q with rightwards harpoon with barb upwards on top minus stack O P with rightwards harpoon with barb upwards on top end cell row blank equals cell open parentheses k comma space l comma space m close parentheses minus open parentheses 2 comma space minus 1 comma space 3 close parentheses end cell row blank equals cell open parentheses k minus 2 comma space l minus open parentheses negative 1 close parentheses comma space m minus 3 close parentheses end cell row blank equals cell open parentheses k minus 2 comma space l plus 1 comma space m minus 3 close parentheses end cell end table

Ingat kembali konsep kesamaan dua buah vektor. Jika diberikan vektor bold italic r equals open parentheses r subscript 1 comma space r subscript 2 comma space r subscript 3 close parentheses dan bold italic s equals open parentheses s subscript 1 comma space s subscript 2 comma space s subscript 3 close parentheses dengan bold italic r equals bold italic s, maka berlaku

table attributes columnalign right center left columnspacing 0px end attributes row cell r subscript 1 end cell equals cell s subscript 1 end cell row cell r subscript 2 end cell equals cell s subscript 2 end cell row cell r subscript 3 end cell equals cell s subscript 3 end cell end table

Terlebih dahulu akan dinyatakan vektor bold italic a sebagai vektor baris yaitu bold italic a equals open parentheses 3 comma space minus 4 comma space 2 close parentheses. Diketahui stack P Q with rightwards harpoon with barb upwards on top berlawanan arah dengan bold italic a, berarti

table attributes columnalign right center left columnspacing 0px end attributes row cell stack P Q with rightwards harpoon with barb upwards on top end cell equals cell negative bold italic a end cell row cell open parentheses k minus 2 comma space l plus 1 comma space m minus 3 close parentheses end cell equals cell negative open parentheses 3 comma space minus 4 comma space 2 close parentheses end cell row cell open parentheses k minus 2 comma space l plus 1 comma space m minus 3 close parentheses end cell equals cell open parentheses negative 3 comma space minus open parentheses negative 4 close parentheses comma space minus 2 close parentheses end cell row cell open parentheses k minus 2 comma space l plus 1 comma space m minus 3 close parentheses end cell equals cell open parentheses negative 3 comma space 4 comma space minus 2 close parentheses end cell end table

Berdasarkan konsep kesamaan dua vektor diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell k minus 2 end cell equals cell negative 3 end cell row k equals cell negative 3 plus 2 end cell row k equals cell negative 1 end cell row blank blank blank row cell l plus 1 end cell equals 4 row l equals cell 4 minus 1 end cell row l equals 3 row blank blank blank row cell m minus 3 end cell equals cell negative 2 end cell row m equals cell negative 2 plus 3 end cell row m equals 1 end table

Sehingga didapat koordinat straight Q yaitu open parentheses k comma space l comma space m close parentheses equals open parentheses negative 1 comma space 3 comma space 1 close parentheses

Dengan demikian, diperoleh koordinat straight Q open parentheses negative 1 comma space 3 comma space 1 close parentheses 

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