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Jika p ⇀ ​ = ⎝ ⎛ ​ − 4 − 2 4 ​ ⎠ ⎞ ​ dan q ⇀ ​ = ⎝ ⎛ ​ 2 − 4 5 ​ ​ ⎠ ⎞ ​ , hasil ∣ p ⇀ ​ ∣ + 2∣ q ⇀ ​ ∣ adalah ...

Jika  dan , hasil  adalah ...

  1. begin mathsize 14px style 20 end style

  2. begin mathsize 14px style 16 end style

  3. size 14px 11

  4. size 14px 6

  5. size 14px 5

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

jawaban yang tepat adalah B.

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Pembahasan

Perhatikan perhitungan berikut ini. Ingat: maka panjang vektor yaitu: panjang vektor yaitu: sehingga Jadi, hasil adalah . Dengan demikian, jawaban yang tepat adalah B.

Perhatikan perhitungan berikut ini.

Ingat:

begin mathsize 14px style open vertical bar stack text a end text with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root end style

maka panjang vektor begin mathsize 14px style stack text p end text with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 4 end cell row cell negative 2 end cell row 4 end table close parentheses end style yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line straight p with rightwards harpoon with barb upwards on top vertical line end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of open parentheses negative 4 close parentheses squared plus left parenthesis negative 2 right parenthesis squared plus 4 to the power of 2 end exponent end root end cell row blank equals cell square root of 16 plus 4 plus 16 end root end cell row blank equals cell square root of 36 end cell row blank equals 6 end table end style

panjang vektor begin mathsize 14px style stack text q end text with rightwards harpoon with barb upwards on top equals open parentheses table row 2 row cell negative 4 end cell row cell square root of 5 end cell end table close parentheses end style yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line straight q with rightwards harpoon with barb upwards on top vertical line end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of 2 squared plus left parenthesis negative 4 right parenthesis squared plus open parentheses square root of 5 close parentheses squared end root end cell row blank equals cell square root of 4 plus 16 plus 5 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table end style

sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line stack text p end text with rightwards harpoon with barb upwards on top vertical line plus 2 vertical line stack text q end text with rightwards harpoon with barb upwards on top vertical line end cell equals cell 6 plus 2 times 5 end cell row blank equals cell 6 plus 10 end cell row blank equals 16 end table end style

Jadi, hasil begin mathsize 14px style vertical line stack text p end text with rightwards harpoon with barb upwards on top vertical line plus 2 vertical line stack text q end text with rightwards harpoon with barb upwards on top vertical line end style adalah begin mathsize 14px style 16 end style.

Dengan demikian, jawaban yang tepat adalah B.

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Segitiga ABC dengan titik koordinat A ( 2 , − 1 , − 3 ) , B ( − 1 , 1 , − 11 ) , dan C ( 4 , − 3 , − 2 ) . p ​ adalah proyeksi vektor ortogonal dari vektor AB pada AC . Vektor p ​ dalam i , j ​ , dan ...

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