Pertanyaan

Hitunglah proyeksi skalar ortogonal a pada b dan juga pada dari vektor-vektor berikut. a. a = ( 2 5 ) dan b = ( 1 7 )

Hitunglah proyeksi skalar ortogonal $a$ pada $b$ dan juga pada dari vektor-vektor berikut.

a. $a = (25)$ dan $b = (17)$

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

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 pada adalah sebagai berikut:

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

Maka,

$begin mathsize 14px style table attributes columnalign right center left end attributes row cell open vertical bar c with rightwards arrow on top close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row space equals cell fraction numerator open parentheses 2 cross times 1 close parentheses plus open parentheses 5 cross times 7 close parentheses over denominator square root of 1 squared plus 7 squared end root end fraction end cell row space equals cell fraction numerator 2 plus 35 over denominator square root of 1 plus 49 end root end fraction end cell row space equals cell fraction numerator 37 over denominator square root of 50 end fraction end cell row space equals cell fraction numerator 37 over denominator 5 square root of 2 end fraction end cell row space equals cell fraction numerator 37 over denominator 5 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row space equals cell fraction numerator 37 square root of 2 over denominator 10 end fraction end cell end table end style$

Maka, proyeksi skalar ortogonal pada adalah $begin mathsize 14px style fraction numerator 37 square root of 2 over denominator 10 end fraction end style$ .

Proyeksi skalar ortogonal pada 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,

$begin mathsize 14px style table attributes columnalign center center left end attributes row cell open vertical bar d with rightwards arrow on top close vertical bar end cell equals cell fraction numerator b with rightwards arrow on top times a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction end cell row space equals cell fraction numerator open parentheses 1 cross times 2 close parentheses plus open parentheses 7 cross times 5 close parentheses over denominator square root of 2 squared plus 5 squared end root end fraction end cell row space equals cell fraction numerator 2 plus 35 over denominator square root of 4 plus 25 end root end fraction end cell row space equals cell fraction numerator 37 over denominator square root of 29 end fraction end cell row space equals cell fraction numerator 37 over denominator square root of 29 end fraction cross times fraction numerator square root of 29 over denominator square root of 29 end fraction end cell row space equals cell fraction numerator 37 square root of 29 over denominator 29 end fraction end cell end table end style$

Maka, proyeksi skalar ortogonal pada adalah $begin mathsize 14px style fraction numerator 37 square root of 29 over denominator 29 end fraction end style$ .

Latihan Bab

Pengertian dan Operasi Vektor I

Operasi Vektor II

Kedudukan Vektor

Aljabar Vektor I