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Pertanyaan

Diketahui tiga buah titik terletak di ruang, yaitu titik A dengan koordinat open parentheses 3 comma space 3 comma space 3 close parentheses, titik B dengan koordinat open parentheses 4 comma space 5 comma space 1 close parentheses, dan titik C dengan koordinat open parentheses 7 comma space 11 comma space minus 5 close parentheses. Ruas-ruas garis berarah stack O A with rightwards arrow on topstack O B with rightwards arrow on top, dan stack O C with rightwards arrow on top berturut-turut mewakili vektor-vektor a with rightwards arrow on topb with rightwards arrow on top, dan c with rightwards arrow on top.

a. Nyatakan vektor a with rightwards arrow on top, vektor b with rightwards arrow on top, dan vektor c with rightwards arrow on top masing-masing dalam bentuk vektor kolom.

b. Nyatakan ruas garis berarah stack A B with rightwards arrow on top, ruas garis berarah stack B C with rightwards arrow on top, dan ruas garis berarah stack A C with rightwards arrow on top, masing-masing dalam bentuk vektor kolom.

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

diperoleh a with rightwards arrow on top equals open parentheses table row 3 row 3 row 3 end table close parenthesesb with rightwards arrow on top equals open parentheses table row 4 row 5 row 1 end table close parenthesesc with rightwards arrow on top equals open parentheses table row 7 row 11 row cell negative 5 end cell end table close parentheses, dan ruas garis berarah stack text AB end text with rightwards arrow on top equals open parentheses table row 1 row 2 row cell negative 2 end cell end table close parenthesesstack text BC end text with rightwards arrow on top equals open parentheses table row 3 row 6 row cell negative 6 end cell end table close parentheses, serta stack text AC end text with rightwards arrow on top equals open parentheses table row 4 row 8 row cell negative 8 end cell end table close parentheses.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah diperoleh a with rightwards arrow on top equals open parentheses table row 3 row 3 row 3 end table close parenthesesb with rightwards arrow on top equals open parentheses table row 4 row 5 row 1 end table close parenthesesc with rightwards arrow on top equals open parentheses table row 7 row 11 row cell negative 5 end cell end table close parentheses, dan ruas garis berarah stack text AB end text with rightwards arrow on top equals open parentheses table row 1 row 2 row cell negative 2 end cell end table close parenthesesstack text BC end text with rightwards arrow on top equals open parentheses table row 3 row 6 row cell negative 6 end cell end table close parentheses, serta stack text AC end text with rightwards arrow on top equals open parentheses table row 4 row 8 row cell negative 8 end cell end table close parentheses.

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 row cell z 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 row cell z subscript b end cell end table close parentheses. Keduanya relatif terhadap titik acuan 0 sehingga vektor posisi dari segmen garis berarah stack text AB end text with rightwards arrow on top dinyatakan dengan rumus:

stack text AB end text with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top equals open parentheses table row cell x subscript b end cell row cell y subscript b end cell row cell z subscript b end cell end table close parentheses minus open parentheses table row cell x subscript a end cell row cell y subscript a end cell row cell z subscript a end cell end table close parentheses

Ingat bahwa untuk titik text P end text di ruang dengan koordinat open parentheses x comma space y comma space z close parentheses berkorespondensi dengan vektor stack text OP end text with rightwards arrow on top equals p with rightwards arrow on top equals open parentheses table row x row y row z end table close parentheses.

a. Untuk titik text A end text dengan koordinat open parentheses 3 comma space 3 comma space 3 close parentheses, maka stack text OA end text with rightwards arrow on top equals a with rightwards arrow on top equals open parentheses table row 3 row 3 row 3 end table close parentheses.

Untuk titik text B end text dengan koordinat open parentheses 4 comma space 5 comma space 1 close parentheses, maka stack text OB end text with rightwards arrow on top equals b with rightwards arrow on top equals open parentheses table row 4 row 5 row 1 end table close parentheses.

Untuk titik text C end text dengan koordinat open parentheses 7 comma space 11 comma space minus 5 close parentheses, maka stack text OC end text with rightwards arrow on top equals c with rightwards arrow on top equals open parentheses table row 7 row 11 row cell negative 5 end cell end table close parentheses.

b. Ruas garis berarah stack text AB end text with rightwards arrow on topstack text BC end text with rightwards arrow on top, dan stack text AC end text with rightwards arrow on top dapat ditentukan sebagai berikut.

Ruas garis berarah stack text AB end text with rightwards arrow on top, yaitu

stack text AB end text with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top equals open parentheses table row 4 row 5 row 1 end table close parentheses minus open parentheses table row 3 row 3 row 3 end table close parentheses equals open parentheses table row 1 row 2 row cell negative 2 end cell end table close parentheses

Jadi, ruas garis berarah stack text AB end text with rightwards arrow on top equals open parentheses table row 1 row 2 row cell negative 2 end cell end table close parentheses

Ruas garis berarah stack text BC end text with rightwards arrow on top, yaitu:

stack text BC end text with rightwards arrow on top equals c with rightwards arrow on top minus b with rightwards arrow on top equals open parentheses table row 7 row 11 row cell negative 5 end cell end table close parentheses minus open parentheses table row 4 row 5 row 1 end table close parentheses equals open parentheses table row 3 row 6 row cell negative 6 end cell end table close parentheses

Jadi, ruas garis berarah stack text BC end text with rightwards arrow on top equals open parentheses table row 3 row 6 row cell negative 6 end cell end table close parentheses

Ruas garis berarah stack text AC end text with rightwards arrow on top, yaitu:

stack text AC end text with rightwards arrow on top equals c with rightwards arrow on top minus a with rightwards arrow on top equals open parentheses table row 7 row 11 row cell negative 5 end cell end table close parentheses minus open parentheses table row 3 row 3 row 3 end table close parentheses equals open parentheses table row 4 row 8 row cell negative 8 end cell end table close parentheses

Jadi, ruas garis berarah stack text AC end text with rightwards arrow on top equals open parentheses table row 4 row 8 row cell negative 8 end cell end table close parentheses.

Dengan demikian, diperoleh a with rightwards arrow on top equals open parentheses table row 3 row 3 row 3 end table close parenthesesb with rightwards arrow on top equals open parentheses table row 4 row 5 row 1 end table close parenthesesc with rightwards arrow on top equals open parentheses table row 7 row 11 row cell negative 5 end cell end table close parentheses, dan ruas garis berarah stack text AB end text with rightwards arrow on top equals open parentheses table row 1 row 2 row cell negative 2 end cell end table close parenthesesstack text BC end text with rightwards arrow on top equals open parentheses table row 3 row 6 row cell negative 6 end cell end table close parentheses, serta stack text AC end text with rightwards arrow on top equals open parentheses table row 4 row 8 row cell negative 8 end cell end table close parentheses.

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Jawaban terverifikasi

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