بِسْـــمِ اللَّهِ الرَّحْمَــنِ الرَّحِيْمِ
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[tex] \vec{u} = \begin{pmatrix} 2 \\ - 3 \\ 4 \end{pmatrix}[/tex]
[tex] \vec{v} = \begin{pmatrix} - 4 \\ - 4 \\ 2 \end{pmatrix}[/tex]
[tex] \rm \vec{p} = \frac{( \vec{u }\: .\: \vec{v}) }{ | \vec{v}|} [/tex]
[tex] \rm \vec{p} = \frac{2 \times ( - 4) + ( - 3) \times( - 4) + 4 \times 2}{{ \sqrt{ {( - 4)}^{2} + {( - 4)}^{2} + {2}^{2}}})}[/tex]
[tex] \rm \vec{p} = \frac{ - 8 + 12 + 8}{{ \sqrt{ {16+ 16 + 4}} } }[/tex]
[tex] \rm \vec{p} = \frac{12}{{ \sqrt{ {36}}} } [/tex]
[tex] \rm \vec{p} = \frac{12}{ 6}[/tex]
[tex] \rm \vec{p} =2[/tex]
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وَاللَّهُ عَالَمُ بِاالصَّوَافَ
Penjelasan dengan langkah-langkah:
u = ( 2,-3, 4 )
v = ( -4, -4, 2)
u.v = (2.–4 –3.–4 + 4.2)
u.v = –8+12+8
u.v = 12
|v| = √[(-4)²+(-4)²+2²]
|v| = √(16+16+4)
|v| = √36 = 6
Proyeksi skalar ortogonal = (u.v)/|v|
= 12/6
