Pertanyaan

Hitunglah proyeksi skalar ortogonal a pada b dan juga pada dari vektor-vektor berikut. d. a = ( − 2 7 ​ ) dan b = ( − 3 5 ​ )

Hitunglah proyeksi skalar ortogonal  pada  dan juga begin mathsize 14px style b with rightwards arrow on top end style pada begin mathsize 14px style a with rightwards arrow on top end style dari vektor-vektor berikut.

d.  dan  

  1. ...space 

  2. ...undefined 

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

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Pembahasan

Proyeksi skalar ortogonal pada adalah sebagai berikut: Maka, Maka, proyeksi skalar ortogonal pada adalah . Proyeksi skalar ortogonal pada adalah sebagai berikut: Maka, Maka, proyeksi skalar ortogonal pada adalah .

Proyeksi skalar ortogonal begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style b with rightwards arrow on top end style adalah sebagai berikut:

begin mathsize 14px style vertical line stack O C with rightwards arrow on top vertical line equals vertical line c with rightwards arrow on top vertical line equals fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator vertical line b with rightwards arrow on top vertical line end fraction end style

Maka,

begin mathsize 14px style table attributes columnalign right center left end attributes row cell vertical line c with rightwards arrow on top vertical line end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator vertical line b with rightwards arrow on top vertical line end fraction end cell row space equals cell fraction numerator left parenthesis negative 2 cross times left parenthesis negative 3 right parenthesis right parenthesis plus left parenthesis 7 cross times 5 right parenthesis over denominator square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis 5 right parenthesis squared end root end fraction end cell row space equals cell fraction numerator 6 plus 35 over denominator square root of 9 plus 25 end root end fraction end cell row space equals cell fraction numerator 41 over denominator square root of 34 end fraction end cell row space equals cell fraction numerator 41 over denominator square root of 34 end fraction cross times fraction numerator square root of 34 over denominator square root of 34 end fraction end cell row space equals cell fraction numerator 41 square root of 34 over denominator 34 end fraction end cell row space space space end table end style 

Maka, proyeksi skalar ortogonal begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style b with rightwards arrow on top end style adalah begin mathsize 14px style fraction numerator 41 square root of 34 over denominator 34 end fraction end style.

Proyeksi skalar ortogonal begin mathsize 14px style b with rightwards arrow on top end style pada begin mathsize 14px style a with rightwards arrow on top end style adalah sebagai berikut:

begin mathsize 14px style vertical line stack O D with rightwards arrow on top vertical line equals vertical line d with rightwards arrow on top vertical line equals fraction numerator b with rightwards arrow on top times a with rightwards arrow on top over denominator vertical line a with rightwards arrow on top vertical line end fraction end style

Maka,

begin mathsize 14px style table attributes columnalign center center left end attributes row cell vertical line d with rightwards arrow on top vertical line end cell equals cell fraction numerator b with rightwards arrow on top times a with rightwards arrow on top over denominator vertical line a with rightwards arrow on top vertical line end fraction end cell row space equals cell fraction numerator left parenthesis negative 3 cross times left parenthesis negative 2 right parenthesis right parenthesis plus left parenthesis 5 cross times 7 right parenthesis over denominator square root of left parenthesis negative 2 right parenthesis squared plus 7 squared end root end fraction end cell row space equals cell fraction numerator 6 plus 35 over denominator square root of 4 plus 49 end root end fraction end cell row space equals cell fraction numerator 41 over denominator square root of 53 end fraction end cell row space equals cell fraction numerator 41 over denominator square root of 53 end fraction cross times fraction numerator square root of 53 over denominator square root of 53 end fraction end cell row space equals cell fraction numerator 41 square root of 53 over denominator 53 end fraction end cell end table end style

Maka, proyeksi skalar ortogonal begin mathsize 14px style b with rightwards arrow on top end style pada begin mathsize 14px style a with rightwards arrow on top end style adalah begin mathsize 14px style fraction numerator 41 square root of 53 over denominator 53 end fraction end style.

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