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

Pertanyaan

Diketahui begin mathsize 14px style u with rightwards arrow on top equals open parentheses table row cell negative sign 2 end cell row cell negative sign 8 end cell row 2 end table close parentheses end style dan begin mathsize 14px style v with rightwards arrow on top equals open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end style. Proyeksi skalar ortogonal begin mathsize 14px style open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses end style pada begin mathsize 14px style v with rightwards arrow on top end style adalah ....

  1. 3

  2. begin mathsize 14px style square root of 3 end style 

  3. 1

  4. begin mathsize 14px style 1 third square root of 3 end style 

  5. begin mathsize 14px style 1 third end style

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top plus v with rightwards arrow on top end cell equals cell open parentheses table row cell negative sign 2 end cell row cell negative sign 8 end cell row 2 end table close parentheses plus open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative sign 2 plus 2 end cell row cell negative sign 8 minus sign 1 end cell row cell 2 minus sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative sign 9 end cell row 0 end table close parentheses end cell end table end style  

Perhatikan bahwa proyeksi skalar ortogonal undefined pada undefined adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses ⋅ v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar end fraction end cell equals cell fraction numerator open parentheses table row 0 row cell negative sign 9 end cell row 0 end table close parentheses ⋅ open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses over denominator square root of 2 squared plus open parentheses negative sign 1 close parentheses squared plus open parentheses negative sign 2 close parentheses squared end root end fraction end cell row blank equals cell fraction numerator 0 ⋅ 2 plus open parentheses negative sign 9 close parentheses ⋅ open parentheses negative sign 1 close parentheses plus 0 ⋅ open parentheses negative sign 2 close parentheses over denominator square root of 4 plus 1 plus 4 end root end fraction end cell row blank equals cell fraction numerator 0 plus 9 plus 0 over denominator square root of 9 end fraction end cell row blank equals cell 9 over 3 end cell row blank equals 3 end table end style  
 

Jadi, jawaban yang tepat adalah A.

80

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