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Diketahui p​=4i−2j​+3k dan q​=2i+j​+k. Nyatakan hasil dari vektor berikut ke dalam vektor kolom. b. 2p​+3q​

Pertanyaan

Diketahui straight p with rightwards arrow on top equals 4 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top dan straight q with rightwards arrow on top equals 2 straight i with rightwards arrow on top plus straight j with rightwards arrow on top plus straight k with rightwards arrow on top. Nyatakan hasil dari vektor berikut ke dalam vektor kolom.spacespacespace

b. 2 straight p with rightwards arrow on top plus 3 straight q with rightwards arrow on topspace

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

 2 straight p with rightwards arrow on top plus 3 straight q with rightwards arrow on top equals open parentheses table row 14 row cell negative 1 end cell row 9 end table close parentheses.space

Pembahasan

b. Jawaban yang benar untuk pertanyaan b adalah 2 straight p with rightwards arrow on top plus 3 straight q with rightwards arrow on top equals open parentheses table row 14 row cell negative 1 end cell row 9 end table close parentheses.space

Jadikan vektor straight p with rightwards arrow on top dan straight q with rightwards arrow on top dalam bentuk vektor kolom terlebih dahulu.space

straight p with rightwards arrow on top equals 4 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top maka straight p with rightwards arrow on top equals open parentheses table row 4 row cell negative 2 end cell row 3 end table close parenthesesspace 

straight q with rightwards arrow on top equals 2 straight i with rightwards arrow on top plus straight j with rightwards arrow on top plus straight k with rightwards arrow on top maka straight q with rightwards arrow on top equals open parentheses table row 2 row 1 row 1 end table close parenthesesspace

Hasil perkalian suatu vektor table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top end cell equals cell open parentheses table row cell straight x subscript 1 end cell row cell straight y subscript 1 end cell row cell straight z subscript 1 end cell end table close parentheses end cell end table dengan straight m suatu skalar yaituspace

 table attributes columnalign right center left columnspacing 0px end attributes row cell straight m straight a with rightwards arrow on top end cell equals cell straight m open parentheses table row cell straight x subscript 1 end cell row cell straight y subscript 1 end cell row cell straight z subscript 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell mx subscript 1 end cell row cell my subscript 1 end cell row cell mz subscript 1 end cell end table close parentheses end cell end tablespace 

Untuk penjumlahan vektor straight p with rightwards arrow on top dan straight q with rightwards arrow on top dilakukan dengan menjumlahkan elemen-elemen yang sejenis.space

table attributes columnalign right center left columnspacing 0px end attributes row cell straight p with rightwards arrow on top plus straight q with rightwards arrow on top end cell equals cell open parentheses table row cell straight x subscript 1 end cell row cell straight y subscript 1 end cell row cell straight z subscript 1 end cell end table close parentheses plus open parentheses table row cell straight x subscript 2 end cell row cell straight y subscript 2 end cell row cell straight z subscript 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell straight x subscript 1 plus straight x subscript 2 end cell row cell straight y subscript 1 plus straight y subscript 2 end cell row cell straight z subscript 1 plus straight z subscript 2 end cell end table close parentheses end cell end tablespace 

Jadi, 2 straight p with rightwards arrow on top plus 3 straight q with rightwards arrow on top dapat ditentuka sebagai berikut:space

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight p with rightwards arrow on top plus 3 straight q with rightwards arrow on top end cell equals cell 2 open parentheses table row 4 row cell negative 2 end cell row 3 end table close parentheses plus 3 open parentheses table row 2 row 1 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 8 row cell negative 4 end cell row 6 end table close parentheses plus open parentheses table row 6 row 3 row 3 end table close parentheses end cell row blank equals cell open parentheses table row 14 row cell negative 1 end cell row 9 end table close parentheses end cell end tablespace 

Dengan demikian, 2 straight p with rightwards arrow on top plus 3 straight q with rightwards arrow on top equals open parentheses table row 14 row cell negative 1 end cell row 9 end table close parentheses.space

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Diketahui vektor p​=⎝⎛​10−2​⎠⎞​, q​=⎝⎛​4−1−2​⎠⎞​, dan r=⎝⎛​0−13​⎠⎞​. Hasil operasi vektor p​−q​+3r adalah ....

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Jawaban terverifikasi

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