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Diketahui vektor p​=(35​), vektor q​=(7−1​), dan vektor r=(−48​). Tentukan: c. 2p​+q​−3r

Pertanyaan

Diketahui vektor p with rightwards arrow on top equals open parentheses table row 3 row 5 end table close parentheses, vektor q with rightwards arrow on top equals open parentheses table row 7 row cell negative 1 end cell end table close parentheses, dan vektor r with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 8 end table close parentheses. Tentukan:
c. 2 p with rightwards arrow on top plus q with rightwards arrow on top minus 3 r with rightwards arrow on top

T. Prita

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jember

Jawaban terverifikasi

Jawaban

hasil perhitungan table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p with rightwards arrow on top plus q with rightwards arrow on top minus 3 r with rightwards arrow on top end cell equals cell open parentheses table row 25 row cell negative 15 end cell end table close parentheses end cell end table.

Pembahasan

Jawaban yang benar dari pertanyaan tersebut adalah  table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p with rightwards arrow on top plus q with rightwards arrow on top minus 3 r with rightwards arrow on top end cell equals cell open parentheses table row 25 row cell negative 15 end cell end table close parentheses end cell end table.

Ingat teori mengenai penjumlahan vektor. Penjumlahan vektor secara aljabar dapat dilakukan dengan cara menjumlahkan komponen yang seletak. Misalkan diketahui vektor a with rightwards arrow on top equals open parentheses table row cell x subscript a end cell row cell y subscript a end cell end table close parentheses dan vektor b with rightwards arrow on top equals open parentheses table row cell x subscript b end cell row cell y subscript b end cell end table close parentheses . Jika c with rightwards arrow on top equals a with rightwards arrow on top plus b with rightwards arrow on top, maka vektor c with rightwards arrow on top ditentukan oleh:

c with rightwards arrow on top equals open parentheses table row cell x subscript a end cell row cell y subscript a end cell end table close parentheses plus open parentheses table row cell x subscript b end cell row cell y subscript b end cell end table close parentheses equals open parentheses table row cell x subscript a plus x subscript b end cell row cell y subscript a plus y subscript b end cell end table close parentheses

Begitupun dengan pengurangan vektor, jika c with rightwards arrow on top equals a with rightwards arrow on top minus b with rightwards arrow on top maka vektor c with rightwards arrow on top ditentukan oleh:

c with rightwards arrow on top equals open parentheses table row cell x subscript a end cell row cell y subscript a end cell end table close parentheses minus open parentheses table row cell x subscript b end cell row cell y subscript b end cell end table close parentheses equals open parentheses table row cell x subscript a minus x subscript b end cell row cell y subscript a minus y subscript b end cell end table close parentheses

Diketahui:
vektor p with rightwards arrow on top equals open parentheses table row 3 row 5 end table close parentheses
vektor q with rightwards arrow on top equals open parentheses table row 7 row cell negative 1 end cell end table close parentheses
vektor r with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 8 end table close parentheses

Hasil perhitungan 2 p with rightwards arrow on top plus q with rightwards arrow on top minus 3 r with rightwards arrow on top:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p with rightwards arrow on top plus q with rightwards arrow on top minus 3 r with rightwards arrow on top end cell equals cell 2 open parentheses table row 3 row 5 end table close parentheses plus open parentheses table row 7 row cell negative 1 end cell end table close parentheses minus 3 open parentheses table row cell negative 4 end cell row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell open parentheses 2 close parentheses open parentheses 3 close parentheses end cell row cell open parentheses 2 close parentheses open parentheses 5 close parentheses end cell end table close parentheses plus open parentheses table row 7 row cell negative 1 end cell end table close parentheses minus open parentheses table row cell negative 12 end cell row 24 end table close parentheses end cell row blank equals cell open parentheses table row 6 row 10 end table close parentheses plus open parentheses table row 7 row cell negative 1 end cell end table close parentheses minus open parentheses table row cell negative 12 end cell row 24 end table close parentheses end cell row blank equals cell open parentheses table row cell 6 plus 7 minus open parentheses negative 12 close parentheses end cell row cell 10 plus open parentheses negative 1 close parentheses minus 24 end cell end table close parentheses end cell row blank equals cell open parentheses table row 25 row cell negative 15 end cell end table close parentheses end cell end table

Dengan demikian hasil perhitungan table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p with rightwards arrow on top plus q with rightwards arrow on top minus 3 r with rightwards arrow on top end cell equals cell open parentheses table row 25 row cell negative 15 end cell end table close parentheses end cell end table.

18

5.0 (3 rating)

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