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Diketahui  dan . Proyeksi skalar ortogonal  pada  adalah....

Pertanyaan

Diketahui begin mathsize 14px style italic u with rightwards arrow on top equals open parentheses table row 0 row 2 row cell negative sign 5 end cell end table close parentheses end style dan begin mathsize 14px style italic v with rightwards arrow on top equals open parentheses table row cell negative sign 2 end cell row 4 row cell negative sign 1 end cell end table close parentheses end style. Proyeksi skalar ortogonal begin mathsize 14px style open parentheses italic u with rightwards arrow on top minus sign v with rightwards arrow on top close parentheses end style pada begin mathsize 14px style open parentheses italic u with rightwards arrow on top plus italic v with rightwards arrow on top close parentheses end style adalah....

  1. begin mathsize 14px style fraction numerator 2 square root of 19 over denominator 19 end fraction end style 

  2. begin mathsize 14px style negative sign fraction numerator 2 square root of 6 over denominator 3 end fraction end style 

  3. begin mathsize 14px style fraction numerator 2 square root of 6 over denominator 3 end fraction end style 

  4. begin mathsize 14px style negative sign fraction numerator 4 square root of 19 over denominator 19 end fraction end style 

  5. begin mathsize 14px style fraction numerator 4 square root of 19 over denominator 19 end fraction end style 

Pembahasan:

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell italic u with rightwards arrow on top minus sign italic v with rightwards arrow on top end cell equals cell open parentheses table row 0 row 2 row cell negative sign 5 end cell end table close parentheses minus sign open parentheses table row cell negative sign 2 end cell row 4 row cell negative sign 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 0 minus sign open parentheses negative sign 2 close parentheses end cell row cell 2 minus sign 4 end cell row cell negative sign 5 minus sign open parentheses negative sign 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative sign 2 end cell row cell negative sign 4 end cell end table close parentheses end cell end table end style 

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell italic u with rightwards arrow on top plus italic v with rightwards arrow on top end cell equals cell open parentheses table row 0 row 2 row cell negative sign 5 end cell end table close parentheses plus open parentheses table row cell negative sign 2 end cell row 4 row cell negative sign 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 0 plus open parentheses negative sign 2 close parentheses end cell row cell 2 plus 4 end cell row cell negative sign 5 plus open parentheses negative sign 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative sign 2 end cell row 6 row cell negative sign 6 end cell end table close parentheses end cell end table end style 

Jadi, proyeksi skalar ortogonal begin mathsize 14px style open parentheses italic u with rightwards arrow on top minus sign italic v with italic rightwards arrow on top close parentheses end style pada undefined adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses italic u with rightwards arrow on top minus sign italic v with rightwards arrow on top close parentheses ⋅ open parentheses italic u with rightwards arrow on top plus italic v with rightwards arrow on top close parentheses over denominator open vertical bar italic u with rightwards arrow on top plus italic v with rightwards arrow on top close vertical bar end fraction end cell equals cell fraction numerator open parentheses table row 2 row cell negative sign 2 end cell row cell negative sign 4 end cell end table close parentheses ⋅ open parentheses table row cell negative sign 2 end cell row 6 row cell negative sign 6 end cell end table close parentheses over denominator square root of open parentheses negative sign 2 close parentheses squared plus 6 squared plus open parentheses negative sign 6 close parentheses squared end root end fraction end cell row blank equals cell fraction numerator 2 ⋅ open parentheses negative sign 2 close parentheses plus open parentheses negative sign 2 close parentheses ⋅ 6 plus open parentheses negative sign 4 close parentheses ⋅ open parentheses negative sign 6 close parentheses over denominator square root of 4 plus 36 plus 36 end root end fraction end cell row blank equals cell fraction numerator negative sign 4 minus sign 12 plus 24 over denominator square root of 76 end fraction end cell row blank equals cell fraction numerator 8 over denominator 2 square root of 19 end fraction end cell end table end style 

Jadi, jawaban yang tepat adalah E.

Jawaban terverifikasi

Dijawab oleh:

A. Rizky

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 06 Januari 2021

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