Misal A(3,5,1) ; B(4,5,7) dan C(4,5,4). Jika 3 vektor AB - vektor CD = 2 vektor BD maka koordinat titik D adalah?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Diket :
a = (3,5,1)
b = (4,5,7)
c = (4,5,4)

tanya :
d = ___?

Jawab :
3.AB - CD = 2.BD
3(b - a) - (d - c) = 2.(d - b)
3b - 3a - d + c = 2d - 2b
- 3a + 3b + 2b + c = 2d + d
- 3a + 5b + c = 3d

d = - a + 5/3.b + 1/3.c

d = - (3,5,1) + 5/3.(4,5,7) + 1/3.(4,5,4)

d = (- 3 + 20/3 + 4/3),(- 5 + 25/3 + 5/3),(- 1 + 35/3 + 4/3)

d = (- 9/3 + 20/3 + 4/3),(- 15/3 + 25/3 + 5/3),(- 3/3 + 35/3 + 4/3)

d = (5,5,12)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
)|(
FZA