Tentukan panjang vektor CD jika: a. A(1,-1,2), B(4,5,2) dan C(1,0,4) Titik D terletak pada AB sehingga AD:DB=2:1 b. A(1,4,3) B(3,3,0) dan C (7,3,-4) Titik D ter

Rumus => AP : PB = m : n => p = (mb + na)/(m + n)

a) A(1,-1,2), B(4,5,2), C(1,0,4)
AD : DB = 2 : 1 => d = (2b + 1a)/(2 + 1)
d = (2(4,5,2) + (1,-1,2))/3 = ((8,10,4) + (1,-1,2))/3 = (9,9,6)/3 = (3,3,2)
CD = d - c = (3,3,2) - (1,0,4) = (2,3,-2)
Panjang CD = |CD| = √(2^2 + 3^2 + (-2)^2) = √(4 + 9 + 4) = √17

b) A(1,4,3), B(3,3,0), C(7,3,-4)
BD : BC = 1 : 3
DB : BC = -1 : 3 => b = (-1c + 3d)/(-1 + 3)
b = (-c + 3d)/2
2b = -c + 3d
2b + c = 3d
d = (2b + c)/3 = (2(3,3,0) + (7,3,-4))/3
= ((6,6,0) + (7,3,-4))/3 = (13,9,-4)/3 = (13/3, 3, -4/3)
CD = d - c = (13/3, 3, -4/3) - (7,3,-4) = (-8/3, 0, 8/3)
Panjang CD = |CD| = √((-8/3)^2 + 0^2 + (8/3)^2)
= √(64/9 + 0 + 64/9) = √(128/9) = √(64.2/9) = 8/3 √2