Diketahui titik A (2,7,8) dan B (-1,1,-1). Titik R membagi AB di dalam sehingga AR=2RB. Panjang vektor AR adalah

jawab

AR  = 2 RB
r - a = 2 (b - r)
r - a = 2b - 2r
3r = a + 2b
r = 1/3 ( a + 2b)
R(x,y, z) = 1/3 { A(x,y,z) + B(2x, 2y, 2z)
rx = 1/3 (2 + 2(-1)) = 1/3 (0)= 0
ry = 1/3 (7 + 2(1)) = 1/3 (9) = 3
rz = 1/3 (8 + 2(-1)) = 1/3 (6) = 2

R = (0, 3, 2)
AR = r- a
AR = { (0-2) , (3-7),(2-8)} = (-2, - 4, - 6)
| AR | = √ { (-2)² +(-4)²+ (-6)²} = √56
|AR| = 2 √14