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Diketahui A(3, 0, 0), B(0, - 3, 0), dan C(0, 0, 4). Panjang vektor proyeksi AC ke vektor AB adalah...

Pertanyaan

Diketahui A(3, 0, 0), B(0, - 3, 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. begin mathsize 12px style fraction numerator square root of 2 over denominator 2 end fraction end style

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

  4. begin mathsize 12px style square root of 2 end style

  5. undefined

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 stylebegin mathsize 12px style open parentheses a subscript 1 comma space a subscript 2 comma space a subscript 3 close parentheses end style dan begin mathsize 12px style Q with rightwards arrow on top end style = begin 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 P with rightwards arrow on top. Q with rightwards arrow on top equals open parentheses a subscript 1 b subscript 1 plus a subscript 2 b subscript 2 plus a subscript 3 b subscript 3 close parentheses  open vertical bar P with rightwards arrow on top close vertical bar equals square root of open parentheses a subscript 1 close parentheses squared plus open parentheses a subscript 2 close parentheses squared plus open parentheses a subscript 3 close parentheses squared end root end style

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

begin mathsize 12px style Z with rightwards arrow on top equals fraction numerator P with rightwards arrow on top. Q with rightwards arrow on top over denominator stack open vertical bar Q close vertical bar with rightwards arrow on top end fraction space space end style

 

Diketahui A(3, 0, 0), B(0, - 3, 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, yaitu:

begin mathsize 12px style stack A C with rightwards arrow on top equals C minus A equals open parentheses table row 0 row 0 row 4 end table close parentheses minus open parentheses table row 3 row 0 row 0 end table close parentheses equals open parentheses table row cell negative 3 end cell row 0 row 4 end table close parentheses  stack A B with rightwards arrow on top equals B minus A equals open parentheses table row 0 row cell negative 3 end cell row 0 end table close parentheses minus open parentheses table row 3 row 0 row 0 end table close parentheses equals open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 0 end table close parentheses end style

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

begin mathsize 12px style Z with rightwards arrow on top equals fraction numerator stack A C with rightwards arrow on top. stack A B with rightwards arrow on top over denominator open vertical bar stack A B with rightwards arrow on top close vertical bar end fraction  Z with rightwards arrow on top equals fraction numerator open parentheses table row cell negative 3 end cell row 0 row 4 end table close parentheses. open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 0 end table close parentheses over denominator square root of open parentheses negative 3 close parentheses squared plus open parentheses negative 3 close parentheses squared plus 0 squared end root end fraction  Z with rightwards arrow on top equals fraction numerator 9 plus 0 plus 0 over denominator square root of 18 end fraction  Z with rightwards arrow on top equals fraction numerator 9 over denominator 3 square root of 2 end fraction  Z with rightwards arrow on top equals fraction numerator 3 over denominator square root of 2 end fraction  Z with rightwards arrow on top equals 3 over 2 square root of 2 end style

Jadi, panjang vektor begin mathsize 12px style stack A C with rightwards arrow on top end style ke begin mathsize 12px style stack A B with rightwards arrow on top end style adalah begin mathsize 12px style 3 over 2 square root of 2 end style

Jawaban terverifikasi

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 05 Oktober 2021

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