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Dari ketiga titik berikut, tentukan manakah yang kolinear. a. A(6, −1, −3), B(8, −4, 3), dan C(0, 8, −21)  b. P(6, 0, −2), Q(3, −2, 8), dan R(1, −3, 2)  c. K(1, −1, 3), L(2, 4, 0), dan M(−2, −16, 12)

Pertanyaan

Dari ketiga titik berikut, tentukan manakah yang kolinear.space

a. straight A open parentheses 6 comma space minus 1 comma space minus 3 close parenthesesstraight B open parentheses 8 comma space minus 4 comma space 3 close parentheses, dan straight C open parentheses 0 comma space 8 comma space minus 21 close parenthesesspace 

b. straight P open parentheses 6 comma space 0 comma space minus 2 close parenthesesstraight Q open parentheses 3 comma space minus 2 comma space 8 close parentheses, dan straight R open parentheses 1 comma space minus 3 comma space 2 close parenthesesspace 

c. straight K open parentheses 1 comma space minus 1 comma space 3 close parenthesesstraight L open parentheses 2 comma space 4 comma space 0 close parentheses, dan straight M open parentheses negative 2 comma space minus 16 comma space 12 close parenthesesspace

U. Istinaro

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

 titik straight K open parentheses 1 comma space minus 1 comma space 3 close parenthesesstraight L open parentheses 2 comma space 4 comma space 0 close parentheses, dan straight M open parentheses negative 2 comma space minus 16 comma space 12 close parenthesesspacekolinear.space

Pembahasan

a. Jawaban yang benar untuk pertanyaan a adalah titik straight A open parentheses 6 comma space minus 1 comma space minus 3 close parenthesesstraight B open parentheses 8 comma space minus 4 comma space 3 close parentheses, dan straight C open parentheses 0 comma space 8 comma space minus 21 close parenthesesspacetidak kolinear.space

Titik straight A comma space straight B comma space dan space straight C kolinear atau segaris jika ada nilai straight kspaceuntuk AC with rightwards arrow on top equals straight k AB with rightwards arrow on top.space 

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell straight b with rightwards arrow on top minus straight a with rightwards arrow on top end cell row blank equals cell open parentheses 8 straight i with rightwards arrow on top minus 4 straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top close parentheses minus open parentheses 6 straight i with rightwards arrow on top minus straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top close parentheses end cell row blank equals cell 2 straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top plus 6 straight k with rightwards arrow on top end cell end tablespace 

table attributes columnalign right center left columnspacing 0px end attributes row cell AC with rightwards arrow on top end cell equals cell straight c with rightwards arrow on top minus straight a with rightwards arrow on top end cell row blank equals cell open parentheses negative 10 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus 5 straight k with rightwards arrow on top close parentheses minus open parentheses 6 straight i with rightwards arrow on top minus straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top close parentheses end cell row blank equals cell negative 16 straight i with rightwards arrow on top minus straight j with rightwards arrow on top plus 8 straight k with rightwards arrow on top end cell end tablespace 

Dari hasil vektor AB with rightwards arrow on top space dan space AC with rightwards arrow on topspacedi atas, dapat diperoleh bahwa:space

 table attributes columnalign right center left columnspacing 0px end attributes row cell AC with rightwards arrow on top end cell not equal to cell straight k AB with rightwards arrow on top end cell row cell negative 16 straight i with rightwards arrow on top minus straight j with rightwards arrow on top plus 8 straight k with rightwards arrow on top end cell not equal to cell 2 straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top plus 6 straight k with rightwards arrow on top end cell end tablespace 

Karena AC with rightwards arrow on top not equal to straight k AB with rightwards arrow on topspacemaka, titik straight A open parentheses 6 comma space minus 1 comma space minus 3 close parenthesesstraight B open parentheses 8 comma space minus 4 comma space 3 close parentheses, dan straight C open parentheses 0 comma space 8 comma space minus 21 close parenthesesspacetidak kolinear.space

Dengan demikian, titik straight A open parentheses 6 comma space minus 1 comma space minus 3 close parenthesesstraight B open parentheses 8 comma space minus 4 comma space 3 close parentheses, dan straight C open parentheses 0 comma space 8 comma space minus 21 close parenthesesspacetidak kolinear.space

b. Jawaban yang benar untuk pertanyaan b adalah titik straight P open parentheses 6 comma space 0 comma space minus 2 close parenthesesstraight Q open parentheses 3 comma space minus 2 comma space 8 close parentheses, dan straight R open parentheses 1 comma space minus 3 comma space 2 close parentheses tidak kolinear.space

Titik straight P comma space straight Q comma space dan space straight Rspacekolinear atau segaris jika ada nilai straight kspaceuntuk PR with rightwards arrow on top equals straight k PQ with rightwards arrow on top.space 

table attributes columnalign right center left columnspacing 0px end attributes row cell PQ with rightwards arrow on top end cell equals cell straight q with rightwards arrow on top minus straight p with rightwards arrow on top end cell row blank equals cell open parentheses 3 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus 8 straight k with rightwards arrow on top close parentheses minus open parentheses 6 straight i with rightwards arrow on top plus 0 straight j with rightwards arrow on top minus 2 straight k with rightwards arrow on top close parentheses end cell row blank equals cell negative 3 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus 10 straight k with rightwards arrow on top end cell end tablespace  

table attributes columnalign right center left columnspacing 0px end attributes row cell PR with rightwards arrow on top end cell equals cell straight r with rightwards arrow on top minus straight p with rightwards arrow on top end cell row blank equals cell open parentheses straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top plus 2 straight k with rightwards arrow on top close parentheses minus open parentheses 6 straight i with rightwards arrow on top plus 0 straight j with rightwards arrow on top minus 2 straight k with rightwards arrow on top close parentheses end cell row blank equals cell negative 5 straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top plus 4 straight k with rightwards arrow on top end cell end tablespace 

Dari hasil vektor PQ with rightwards arrow on top space dan space PR with rightwards arrow on topspacedi atas, dapat diperoleh bahwa:space

table attributes columnalign right center left columnspacing 0px end attributes row cell PR with rightwards arrow on top end cell not equal to cell straight k PQ with rightwards arrow on top end cell row cell negative 5 straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top plus 4 straight k with rightwards arrow on top end cell not equal to cell negative 3 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus 10 straight k with rightwards arrow on top end cell end tablespace  

Karena PR with rightwards arrow on top not equal to straight k PQ with rightwards arrow on topspacemaka, titik straight P open parentheses 6 comma space 0 comma space minus 2 close parenthesesstraight Q open parentheses 3 comma space minus 2 comma space 8 close parentheses, dan straight R open parentheses 1 comma space minus 3 comma space 2 close parenthesesspacetidak kolinear.space

Dengan demikian, titik straight P open parentheses 6 comma space 0 comma space minus 2 close parenthesesstraight Q open parentheses 3 comma space minus 2 comma space 8 close parentheses, dan straight R open parentheses 1 comma space minus 3 comma space 2 close parentheses tidak kolinear.space

c. Jawaban yang benar untuk pertanyaan c adalah titik straight K open parentheses 1 comma space minus 1 comma space 3 close parenthesesstraight L open parentheses 2 comma space 4 comma space 0 close parentheses, dan straight M open parentheses negative 2 comma space minus 16 comma space 12 close parenthesesspacekolinear.space 

Titik straight K comma space straight L comma space dan space straight Mspacekolinear atau segaris jika ada nilai straight kspaceuntuk KM with rightwards arrow on top equals straight k KL with rightwards arrow on top.space 

table attributes columnalign right center left columnspacing 0px end attributes row cell KL with rightwards arrow on top end cell equals cell straight l with rightwards arrow on top minus straight k with rightwards arrow on top end cell row blank equals cell open parentheses 2 straight i with rightwards arrow on top plus 4 straight j with rightwards arrow on top plus 0 straight k with rightwards arrow on top close parentheses minus open parentheses straight i with rightwards arrow on top minus straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top close parentheses end cell row blank equals cell straight i with rightwards arrow on top plus 5 straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top end cell end tablespace 

table attributes columnalign right center left columnspacing 0px end attributes row cell KM with rightwards arrow on top end cell equals cell straight m with rightwards arrow on top minus straight k with rightwards arrow on top end cell row blank equals cell open parentheses negative 2 straight i with rightwards arrow on top minus 16 straight j with rightwards arrow on top plus 12 straight k with rightwards arrow on top close parentheses minus open parentheses straight i with rightwards arrow on top minus straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top close parentheses end cell row blank equals cell negative 3 straight i with rightwards arrow on top minus 15 straight j with rightwards arrow on top plus 9 straight k with rightwards arrow on top end cell end tablespace 

Dari hasil vektor KL with rightwards arrow on top space dan space KM with rightwards arrow on topspacedi atas, dapat diperoleh bahwa:space 

table attributes columnalign right center left columnspacing 0px end attributes row cell KM with rightwards arrow on top end cell equals cell straight k KL with rightwards arrow on top end cell row cell negative 3 straight i with rightwards arrow on top minus 15 straight j with rightwards arrow on top plus 9 straight k with rightwards arrow on top end cell equals cell open parentheses negative 3 close parentheses open parentheses straight i with rightwards arrow on top plus 5 straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top close parentheses end cell end tablespace space  

Karena KM with rightwards arrow on top not equal to straight k KL with rightwards arrow on topspacedengan nilai straight k equals negative 3 maka, titik straight K open parentheses 1 comma space minus 1 comma space 3 close parenthesesstraight L open parentheses 2 comma space 4 comma space 0 close parentheses, dan straight M open parentheses negative 2 comma space minus 16 comma space 12 close parenthesesspacekolinear.space

Dengan demikian, titik straight K open parentheses 1 comma space minus 1 comma space 3 close parenthesesstraight L open parentheses 2 comma space 4 comma space 0 close parentheses, dan straight M open parentheses negative 2 comma space minus 16 comma space 12 close parenthesesspacekolinear.space

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