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Diketahui A(4, 0, 0), B(0, -4, 0), dan C(0, 0, 4). Panjang vektor proyeksi AC ke vektor AB adalah...

Pertanyaan

Diketahui A(4, 0, 0), B(0, -4, 0), dan C(0, 0, 4). Panjang vektor proyeksi begin mathsize 12px style stack A C with rightwards arrow on top end style ke vektor begin mathsize 12px style stack A B with rightwards arrow on top end style adalah...

  1. begin mathsize 12px style fraction numerator 3 square root of 2 over denominator 2 end fraction end style

  2. fraction numerator square root of size 12px 2 over denominator size 12px 2 end fraction

  3. fraction numerator square root of size 12px 2 over denominator size 12px 3 end fraction

  4. size 12px 2 square root of size 12px 2

  5. fraction numerator square root of size 12px 3 over denominator size 12px 2 end fraction

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Jawaban terverifikasi

Pembahasan

Jika titik Pbegin mathsize 12px style open parentheses a subscript 1 comma space a subscript 2 comma space a subscript 3 close parentheses end style dan Qbegin mathsize 12px style open parentheses b subscript 1 comma space b subscript 2 comma space b subscript 3 close parentheses end style , maka:

begin mathsize 12px style stack P Q with rightwards arrow on top equals Q minus P equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell row cell b subscript 3 end cell end table close parentheses minus open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell row cell a subscript 3 end cell end table close parentheses end style

Misal: begin mathsize 12px style P with rightwards arrow on top end style = begin mathsize 12px style open parentheses a subscript 1 comma space a subscript 2 comma space a subscript 3 close parentheses end style dan size 12px Q with size 12px rightwards arrow on top = open parentheses size 12px b subscript size 12px 1 size 12px comma size 12px space size 12px b subscript size 12px 2 size 12px comma size 12px space size 12px b subscript size 12px 3 close parentheses, maka:

begin mathsize 12px style P with rightwards arrow on top end style . size 12px Q with size 12px rightwards arrow on top = open parentheses size 12px a subscript size 12px 1 size 12px b subscript size 12px 1 size 12px plus size 12px a subscript size 12px 2 size 12px b subscript size 12px 2 size 12px plus size 12px a subscript size 12px 3 size 12px b subscript size 12px 3 close parentheses

open vertical bar size 12px P with size 12px rightwards arrow on top close vertical bar size 12px equals square root of open parentheses size 12px a subscript size 12px 1 close parentheses to the power of size 12px 2 size 12px plus open parentheses size 12px a subscript size 12px 2 close parentheses to the power of size 12px 2 size 12px plus open parentheses size 12px a subscript size 12px 3 close parentheses to the power of size 12px 2 end root

 

Misal size 12px Z with size 12px rightwards arrow on top adalah Proyeksi skalar vektor begin mathsize 12px style P with rightwards arrow on top end style pada vektor size 12px Q with size 12px rightwards arrow on top, maka:

size 12px Z with size 12px rightwards arrow on top size 12px equals fraction numerator size 12px P with size 12px rightwards arrow on top size 12px. size 12px Q with size 12px rightwards arrow on top over denominator open vertical bar size 12px Q with size 12px rightwards arrow on top close vertical bar end fraction

 

Diketahui A(4, 0, 0), B(0, -4, 0), dan C(0, 0, 4). Panjang vektor proyeksi begin mathsize 12px style stack A C with rightwards arrow on top end style ke vektor stack size 12px A size 12px B with size 12px rightwards arrow on top, yaitu:

stack size 12px A size 12px C with size 12px rightwards arrow on top size 12px equals size 12px C size 12px minus size 12px A size 12px equals open parentheses table row size 12px 0 row size 12px 0 row size 12px 4 end table close parentheses size 12px minus open parentheses table row size 12px 4 row size 12px 0 row size 12px 0 end table close parentheses size 12px equals open parentheses table row cell size 12px minus size 12px 4 end cell row size 12px 0 row size 12px 4 end table close parentheses  stack size 12px A size 12px B with size 12px rightwards arrow on top size 12px equals size 12px B size 12px minus size 12px A size 12px equals open parentheses table row size 12px 0 row cell size 12px minus size 12px 4 end cell row size 12px 0 end table close parentheses size 12px minus open parentheses table row size 12px 4 row size 12px 0 row size 12px 0 end table close parentheses size 12px equals open parentheses table row cell size 12px minus size 12px 4 end cell row cell size 12px minus size 12px 4 end cell row size 12px 0 end table close parentheses

Misal undefined adalah proyeksi vektor begin mathsize 12px style stack A C with rightwards arrow on top end style ke undefined, maka:

size 12px Z with size 12px rightwards arrow on top size 12px equals fraction numerator stack size 12px A size 12px C with size 12px rightwards arrow on top size 12px. stack size 12px A size 12px B with size 12px rightwards arrow on top over denominator open vertical bar stack size 12px A size 12px B with size 12px rightwards arrow on top close vertical bar end fraction size 12px equals fraction numerator open parentheses table row cell size 12px minus size 12px 4 end cell row size 12px 0 row size 12px 4 end table close parentheses size 12px times open parentheses table row cell size 12px minus size 12px 4 end cell row cell size 12px minus size 12px 4 end cell row size 12px 4 end table close parentheses over denominator square root of open parentheses size 12px minus size 12px 4 close parentheses to the power of size 12px 2 size 12px plus open parentheses size 12px minus size 12px 4 close parentheses to the power of size 12px 2 size 12px plus size 12px 0 to the power of size 12px 2 end root end fraction  size 12px Z with size 12px rightwards arrow on top size 12px equals fraction numerator size 12px 16 size 12px plus size 12px 0 size 12px plus size 12px 0 over denominator square root of size 12px 32 end fraction  size 12px Z with size 12px rightwards arrow on top size 12px equals fraction numerator size 12px 16 over denominator size 12px 4 square root of size 12px 2 end fraction  size 12px Z with size 12px rightwards arrow on top size 12px equals fraction numerator size 12px 4 over denominator square root of size 12px 2 end fraction  size 12px Z with size 12px rightwards arrow on top size 12px equals size 12px 2 square root of size 12px 2

 

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