diketahui vektor a = 2i+j-9k ,b=i-j+3k ,c=3i+2j+k dan d = a +2b Proyeksi vektor ortogonal vektor d pada vektor c adalah

d = a+2b = (2i+j-9k) + 2(i-j+3k) = (2i+j-9k) + (2i-2j+6k) = 4i-j-3k
c.d = (3.4) + (2.-1) + (1.-3) = 12 + (-2) + (-3) = 7
|c| = [tex] \sqrt{ 3^{2}+ 2^{2}+ 1^{2}} = \sqrt{9+4+1} = \sqrt{14}[/tex]
[tex] \frac{c.d}{ |c|^{2}} . c = \frac{7}{(\sqrt{14}^{2})} . (3i+2j+k) = \frac{7}{14} . (3i+2j+k) = \frac{1}{2} . 3i+ 2j+ k[/tex] [tex]= \frac{3}{2} i + j + \frac{1}{2} k[/tex]