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Diketahui titik P(2,5,3). Tentukan cosinus arah garis OP!

Pertanyaan

Diketahui titik begin mathsize 14px style straight P left parenthesis 2 comma space 5 comma space 3 right parenthesis end style. Tentukan cosinus arah garis OP!

Pembahasan Soal:

Pertama tentukan panjang vektor satuan titik P.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar OP with rightwards arrow on top close vertical bar end cell equals cell square root of 2 squared plus 5 squared plus 3 squared end root end cell row blank equals cell square root of 4 plus 25 plus 9 end root end cell row blank equals cell square root of 38 end cell end table end style 

Maka cosinus arah dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell OP with rightwards arrow on top end cell end table end style adalah

begin mathsize 14px style cos space straight alpha equals fraction numerator 2 over denominator square root of 38 end fraction cos space straight beta equals fraction numerator 5 over denominator square root of 38 end fraction cos space straight gamma equals fraction numerator 3 over denominator square root of 38 end fraction end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Janatu

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui titik A(5,−3,4), B(1,5,−7), dan titik C(−4,−6,2). Nyatakan vektor-vektor berikut dalam bentuk vektor basis kemudian tentukan panjang masing-masing vektor tersebut. a. AB

Pembahasan Soal:

Vektor basis dan panjang vektor.

table attributes columnalign right center left columnspacing 2px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row cell Vektor space basis space AB with rightwards arrow on top end cell rightwards arrow cell AB with rightwards arrow on top equals x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top end cell row cell Panjang space vektor space AB with rightwards arrow on top end cell rightwards arrow cell open vertical bar AB with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root end cell end table

Diketahui:

Titik straight A open parentheses 5 comma space minus 3 comma space 4 close parenthesesstraight B open parentheses 1 comma space 5 comma space minus 7 close parentheses, dan straight C open parentheses negative 4 comma space minus 6 comma space 2 close parentheses.

Akan ditentukan vektor basis dan panjang vekto AB with rightwards arrow on top.

Terlebih dahulu tentukan AB with rightwards arrow on top.

AB with rightwards arrow on top equals straight B minus straight A equals open parentheses 1 minus 5 comma space 5 minus open parentheses negative 3 close parentheses comma space minus 7 minus 4 close parentheses equals open parentheses negative 4 comma space 8 comma space minus 11 close parentheses

Sehingga diperoleh vektor basisnya adalah AB with rightwards arrow on top equals negative 4 i with rightwards arrow on top plus 8 j with rightwards arrow on top minus 11 k with rightwards arrow on top.

Menghitung panjang vektor AB with rightwards arrow on top.

table attributes columnalign right center left columnspacing 2px end attributes row cell open vertical bar AB with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 4 close parentheses squared plus open parentheses 8 close parentheses squared plus open parentheses negative 11 close parentheses squared end root end cell row blank equals cell square root of 16 plus 64 plus 121 end root end cell row cell open vertical bar AB with rightwards arrow on top close vertical bar end cell equals cell square root of 201 end cell end table

Diperoleh panjang vektornya adalah square root of 201.

0

Roboguru

Diketahui titik A(5,−3,4), B(1,5,−7), dan titik C(−4,−6,2). Nyatakan vektor-vektor berikut dalam bentuk vektor basis kemudian tentukan panjang masing-masing vektor tersebut. b. BA

Pembahasan Soal:

Vektor basis dan panjang vektor.

table attributes columnalign right center left columnspacing 2px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row cell Vektor space basis space AB with rightwards arrow on top end cell rightwards arrow cell AB with rightwards arrow on top equals x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top end cell row cell Panjang space vektor space AB with rightwards arrow on top end cell rightwards arrow cell open vertical bar AB with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root end cell end table

Diketahui:

Titik straight A open parentheses 5 comma space minus 3 comma space 4 close parenthesesstraight B open parentheses 1 comma space 5 comma space minus 7 close parentheses, dan straight C open parentheses negative 4 comma space minus 6 comma space 2 close parentheses.

Akan ditentukan vektor basis dan panjang vekto BA with rightwards arrow on top.

Terlebih dahulu tentukan BA with rightwards arrow on top.

BA with rightwards arrow on top equals straight A minus straight B equals open parentheses 5 minus 1 comma space minus 3 minus 5 comma space 4 minus open parentheses negative 7 close parentheses close parentheses equals open parentheses 4 comma space minus 8 comma space 11 close parentheses

Sehingga diperoleh vektor basisnya adalah BA with rightwards arrow on top equals 4 i with rightwards arrow on top minus 8 j with rightwards arrow on top plus 11 k with rightwards arrow on top.

Menghitung panjang vektor BA with rightwards arrow on top.

table attributes columnalign right center left columnspacing 2px end attributes row cell open vertical bar BA with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses 4 close parentheses squared plus open parentheses negative 8 close parentheses squared plus open parentheses 11 close parentheses squared end root end cell row blank equals cell square root of 16 plus 64 plus 121 end root end cell row cell open vertical bar BA with rightwards arrow on top close vertical bar end cell equals cell square root of 201 end cell end table

Diperoleh panjang vektornya adalah square root of 201.

0

Roboguru

Diberikan titik-titik  dan  . Jika ruas garis berarah  dan  berturut-turut mewakili vektor-vektor udanv maka nilai dari

Pembahasan Soal:

Diketahui

u with rightwards arrow on top equals stack A B with rightwards arrow on top equals open parentheses table row cell x subscript B minus x subscript A end cell row cell y subscript B minus y subscript A end cell row cell z subscript B minus z subscript A end cell end table close parentheses equals open parentheses table row cell negative 1 minus 2 end cell row cell 3 minus 6 end cell row cell 7 minus open parentheses negative 5 close parentheses end cell end table close parentheses equals open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses    v with rightwards arrow on top equals stack B C with rightwards arrow on top equals open parentheses table row cell x subscript C minus x subscript B end cell row cell y subscript C minus y subscript B end cell row cell z subscript C minus z subscript B end cell end table close parentheses equals open parentheses table row cell 4 minus open parentheses negative 1 close parentheses end cell row cell negative 1 minus 3 end cell row cell 8 minus 7 end cell end table close parentheses equals open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses    u with rightwards arrow on top plus v with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses plus open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses equals open parentheses table row 2 row cell negative 7 end cell row 13 end table close parentheses

Sehingga

open vertical bar u with rightwards arrow on top plus v with rightwards arrow on top close vertical bar squared equals open parentheses square root of 2 squared plus open parentheses negative 7 close parentheses squared plus 13 squared end root close parentheses squared equals open parentheses square root of 4 plus 49 plus 169 end root close parentheses squared equals open parentheses square root of 222 close parentheses squared equals 222

0

Roboguru

Jika diketahui vektor a⇀=4i⇀−j⇀​+2k⇀ dan b⇀=4i⇀−2j⇀​−5k⇀, maka panjang vektor a⇀−2b⇀= ...

Pembahasan Soal:

Diperoleh:

table attributes columnalign center center left center center center center end attributes row cell a with rightwards harpoon with barb upwards on top end cell equals cell 4 i with rightwards harpoon with barb upwards on top minus j with rightwards harpoon with barb upwards on top plus 2 k with rightwards harpoon with barb upwards on top end cell rightwards arrow cell a with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 4 row cell negative 1 end cell row 2 end table close parentheses end cell row cell b with rightwards harpoon with barb upwards on top end cell equals cell 4 i with rightwards harpoon with barb upwards on top minus 2 j with rightwards harpoon with barb upwards on top minus 5 k with rightwards harpoon with barb upwards on top end cell rightwards arrow cell b with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 4 row cell negative 2 end cell row cell negative 5 end cell end table close parentheses end cell end table

Kemudian operasikan bentuk vektor.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 4 row cell negative 1 end cell row 2 end table close parentheses minus 2 open parentheses table row 4 row cell negative 2 end cell row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative 1 end cell row 2 end table close parentheses minus open parentheses table row 8 row cell negative 4 end cell row cell negative 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 8 end cell row cell negative 1 minus open parentheses negative 4 close parentheses end cell row cell 2 minus open parentheses negative 10 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row cell negative 1 plus 4 end cell row cell 2 plus 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 3 row 12 end table close parentheses end cell end table

Panjang vektor a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top end cell equals cell open vertical bar a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top close vertical bar end cell row blank equals cell square root of open parentheses negative 4 close parentheses squared plus open parentheses 3 close parentheses squared plus open parentheses 12 close parentheses squared end root end cell row blank equals cell square root of 16 plus 9 plus 144 end root end cell row blank equals cell square root of 169 end cell row blank equals 13 end table

Maka, panjang vektor a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top equals 13.

0

Roboguru

Diketahui titik A(5,−3,4), B(1,5,−7), dan titik C(−4,−6,2). Nyatakan vektor-vektor berikut dalam bentuk vektor basis kemudian tentukan panjang masing-masing vektor tersebut. d. CA

Pembahasan Soal:

Vektor basis dan panjang vektor.

table attributes columnalign right center left columnspacing 2px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row cell Vektor space basis space AB with rightwards arrow on top end cell rightwards arrow cell AB with rightwards arrow on top equals x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top end cell row cell Panjang space vektor space AB with rightwards arrow on top end cell rightwards arrow cell open vertical bar AB with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root end cell end table

Diketahui:

Titik straight A open parentheses 5 comma space minus 3 comma space 4 close parenthesesstraight B open parentheses 1 comma space 5 comma space minus 7 close parentheses, dan straight C open parentheses negative 4 comma space minus 6 comma space 2 close parentheses.

Akan ditentukan vektor basis dan panjang vekto CA with rightwards arrow on top.

Terlebih dahulu tentukan CA with rightwards arrow on top.

CA with rightwards arrow on top equals straight C minus straight A equals open parentheses negative 4 minus 5 comma space minus 6 minus open parentheses negative 3 close parentheses comma space 2 minus 4 close parentheses equals open parentheses negative 9 comma space minus 3 comma space minus 2 close parentheses

Sehingga diperoleh vektor basisnya adalah CA with rightwards arrow on top equals negative 9 straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top minus 2 straight k with rightwards arrow on top.

Menghitung panjang vektor CA with rightwards arrow on top.

table attributes columnalign right center left columnspacing 2px end attributes row cell open vertical bar CA with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 9 close parentheses squared plus open parentheses negative 3 close parentheses squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 81 plus 9 plus 4 end root end cell row cell open vertical bar CA with rightwards arrow on top close vertical bar end cell equals cell square root of 94 end cell end table

Diperoleh panjang vektornya adalah square root of 94.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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